#### Study sets matching "algebra chapter 6 inequalities"

#### Study sets matching "algebra chapter 6 inequalities"

System of linear equations

Solution of a system of linear equations

Consistent system

Independent system

Two or more linear equations using the same variables.

Any ordered pair that makes all of the inequalities in the sy…

A system of equations that has at least one solution is consi…

A system of linear equations that has a unique solution.

System of linear equations

Two or more linear equations using the same variables.

Solution of a system of linear equations

Any ordered pair that makes all of the inequalities in the sy…

Boundary

Compound Inequality

Inequality

Intersection

A line or curve that separates the coordinate plane into regi…

Two or more inequalities that are connected by the words "and…

An open sentence that contains the symbol ˂, >, ≤, or ≥

The graph of a compound inequality containing and; the soluti…

Boundary

A line or curve that separates the coordinate plane into regi…

Compound Inequality

Two or more inequalities that are connected by the words "and…

systems of equations

consistent system of equations

Independent system of equations

dependent system of equations

Set of equations with the same variable

A system of equations that is said to have exactly one soluti…

A consistent system of equations with exactly one solution

A system of equations that has an infinite number of solutions.

systems of equations

Set of equations with the same variable

consistent system of equations

A system of equations that is said to have exactly one soluti…

Solution of an inequality

Equivalent inequalities

Roster form

Set-builder notation

Any value or values of a variable in the inequality that make…

Inequalities that have the same set of solutions.

A notation for listing all of the elements in a set using set…

A notation used to describe the elements of a set.

Solution of an inequality

Any value or values of a variable in the inequality that make…

Equivalent inequalities

Inequalities that have the same set of solutions.

Literal Equations

Complex Numbers

The Complex Number √-1

The Complex Number i^2

equations that are all or mostly all variables

a number written in the form (a + bi) where a and b are Real…

= i

= -1

Literal Equations

equations that are all or mostly all variables

Complex Numbers

a number written in the form (a + bi) where a and b are Real…

Addition Property of Inequality

Division Property of Inequality

Inequality

Multiplication Property of Inequality

The Addition Property of Inequality states that if you add th…

The Division Property of Inequality states that is you divide…

An inequality is a mathematical sentence that contains one of…

The Multiplication Property of Inequality states that if you…

Addition Property of Inequality

The Addition Property of Inequality states that if you add th…

Division Property of Inequality

The Division Property of Inequality states that is you divide…

arithmetic sequence

dependent variable

function

function rule

add the same number to the previous term (pattern)

depends on the input value (output)

a relation that assigns exactly one output value to one input…

describes the relationship between each input and output.

arithmetic sequence

add the same number to the previous term (pattern)

dependent variable

depends on the input value (output)

equation

Substitute

Solution

Balance

A mathematical sentence stating that two quantities are equal

Replace a variable with a given real number.

The value of the variable that makes the equations true.

When both sides have the same quantity or mass. 3 + 16 = 19

equation

A mathematical sentence stating that two quantities are equal

Substitute

Replace a variable with a given real number.

Addition Property of Equality

Addition Property of Inequality

coefficient

Division Property of Equality

If you add the same number to each side of an equation, the t…

If you add the same number to each side of an inequality, the…

The numerical factor of a term that contains a variable.

If you divide each side of an equation by the same nonzero nu…

Addition Property of Equality

If you add the same number to each side of an equation, the t…

Addition Property of Inequality

If you add the same number to each side of an inequality, the…

first differences

solution

intersection point

compound inequality

determined by calculating the difference between successive p…

any value that makes the open sentence true

the ordered pair that satisfies both functions at the same time

an inequality that is formed by the union, "or," or the inter…

first differences

determined by calculating the difference between successive p…

solution

any value that makes the open sentence true

system of linear equations

solution of the system of linear equat…

no solution

infinitely many solutions

A set of two or more linear equations containing two or more…

The intersection point of the two lines

a system of equations in which there are no solutions (the li…

The number of solutions of a system of equations in which the…

system of linear equations

A set of two or more linear equations containing two or more…

solution of the system of linear equat…

The intersection point of the two lines

consistent

dependent

elimination method

inconsistent

A system of equations that has at least one solution

A consistent system that has infinitely many solutions.

If a=b and c=d, then a+c=b+d and a-c=b-d. In this method, you…

A system of equations that has no solution.

consistent

A system of equations that has at least one solution

dependent

A consistent system that has infinitely many solutions.

Addition Property of Equality

Addition Property of Inequality

coefficient

Division Property of Equality

If you add the same number to each side of an equation, the t…

If you add the same number to each side of an inequality, the…

The numerical factor of a term that contains a variable.

If you divide each side of an equation by the same nonzero nu…

Addition Property of Equality

If you add the same number to each side of an equation, the t…

Addition Property of Inequality

If you add the same number to each side of an inequality, the…

Properties of Inequalities

Theorem 6-1 - The Exterior Angle Inequ…

Statement

Converse

1. If a > b and c >= d, then a + c > b + d... 2. If a > b and c…

The measure of an exterior angle of a triangle is greater tha…

If P, then q

If Q, then P

Properties of Inequalities

1. If a > b and c >= d, then a + c > b + d... 2. If a > b and c…

Theorem 6-1 - The Exterior Angle Inequ…

The measure of an exterior angle of a triangle is greater tha…

composite function

index of a radical

inverse function

inverse relation

a function formed by evaluating one function with another fun…

the part of a radical that gives the degree of the root.

a function that "undoes" what the original function does.

a relationship in which one variable decreases when another v…

composite function

a function formed by evaluating one function with another fun…

index of a radical

the part of a radical that gives the degree of the root.

Exterior Angle Inequality Theorem

Indirect Proof

Bigger Angle Theorem

Longer Side Theorem

The measure of an exterior angle of a triangle is greater tha…

Always begins by assuming what is to be proven is false. Then…

If two sides of a triangle are NOT congruent, then the larger…

If two angles of a triangle are NOT congruent then the longer…

Exterior Angle Inequality Theorem

The measure of an exterior angle of a triangle is greater tha…

Indirect Proof

Always begins by assuming what is to be proven is false. Then…

axis of symmetry

parabola

square root property

completing the square

a line about which a figure is symmetric

the set of all points in plane that are the same distance fro…

for any real number n, if x squared = n, the x = plus or minu…

a process used to make a quadratic expression into a perfect…

axis of symmetry

a line about which a figure is symmetric

parabola

the set of all points in plane that are the same distance fro…

System of Linear Equations

Solution of a system of linear equations

Substitution Method

Elimination Method

two or more linear equations

The ordered pair that makes all the equations in a system true

When you solve one of the equations in the system for x or y,…

When you add or subtract the linear equations so that one var…

System of Linear Equations

two or more linear equations

Solution of a system of linear equations

The ordered pair that makes all the equations in a system true

The measure of an exterior angle of a…

If one side of a triangle is longer th…

If one angle of a triangle is larger t…

The perpendicular segment from a point…

...greater than the measure of either remote interior angle.

...the angle opposite the first side is larger than the angle…

...the side opposite the first angle is longer than the side…

...the shortest segment from the point to the line.

The measure of an exterior angle of a…

...greater than the measure of either remote interior angle.

If one side of a triangle is longer th…

...the angle opposite the first side is larger than the angle…

elimination method

linear inequality

solution of a system of linear inequal…

solution of a system of linear equations

solving systems by adding or subtracting equations to elimina…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.…

a set of values that make all equations in a system true. [p.…

elimination method

solving systems by adding or subtracting equations to elimina…

linear inequality

an inequality in two variables whose graph is a region of the…

*KeyConcepts*

Systems of Equations

Systems of Inequalities

*KeyVocabulary*

...

-a system with a graph of two intersecting lines has one solu…

-a system of inequalities is a set of two or more inequalitie…

...

*KeyConcepts*

...

Systems of Equations

-a system with a graph of two intersecting lines has one solu…

Solving Systems of Equations Using Sub…

Solving Systems of Equations by Adding…

Solving Systems of Equations by Multip…

Solving Systems of Equations from Word…

Step 1: Solve one equation for x (or y).... Step 2: Substitute t…

Step 1: Line up columns of x's, y's, and constant numbers.... St…

Step 1: Line up columns of x's, y's, and constant numbers.... St…

Step 1: Read and reread the word problem while underlining, c…

Solving Systems of Equations Using Sub…

Step 1: Solve one equation for x (or y).... Step 2: Substitute t…

Solving Systems of Equations by Adding…

Step 1: Line up columns of x's, y's, and constant numbers.... St…

5 Properties of Inequality

The Exterior Angle Inequality Thm

Conditional

Contrapositive

1. if a > b and c>= d then a+c > b+d... 2. if a > b and c > 0 th…

the measure of an exterior angle of a triangle is greater tha…

if p then q

if not q then not p

5 Properties of Inequality

1. if a > b and c>= d then a+c > b+d... 2. if a > b and c > 0 th…

The Exterior Angle Inequality Thm

the measure of an exterior angle of a triangle is greater tha…

Equation

Solution

Equivalent equation

Subtraction Property of Equality

A mathematical sentence that contains an equal sign, = , stat…

A replacement value for the variable in an open sentence. A v…

Two or more equations with the same solution.

If you subtract the same number from each side of an equation…

Equation

A mathematical sentence that contains an equal sign, = , stat…

Solution

A replacement value for the variable in an open sentence. A v…

Inequalities

Signs of Inequalities

Types of Inequalities

Linear Inequality

The relation between two expressions that are not equal, empl…

< and > are used open circle.... ≤ and ≥ are used closed circle.

There are two types of Inequalities - Linear Inequalities and…

A Linear inequality is an inequality which involves a linear…

Inequalities

The relation between two expressions that are not equal, empl…

Signs of Inequalities

< and > are used open circle.... ≤ and ≥ are used closed circle.

5 Properties of Inequality

The Exterior Angle Inequality Thm

Conditional

Contrapositive

1. if a > b and c>= d then a+c > b+d... 2. if a > b and c > 0 th…

the measure of an exterior angle of a triangle is greater tha…

if p then q

if not q then not p

5 Properties of Inequality

1. if a > b and c>= d then a+c > b+d... 2. if a > b and c > 0 th…

The Exterior Angle Inequality Thm

the measure of an exterior angle of a triangle is greater tha…

linear function

linear equation

y intercept

x intercept

a function whose graph forms a straight line Ax + By = C

any equation that can be written in standard form Ax + By = C

the y-coordinate where the graph intersects the y-axis, b (0,…

the x-coordinate where the graph intersects the x-axis (x, 0)

linear function

a function whose graph forms a straight line Ax + By = C

linear equation

any equation that can be written in standard form Ax + By = C

nth root

principal root

index

radicand

for any real numbers "a" and "b", and any positive integer "n…

when a radical has two answers , the positive answer

in a radical, it indicates the degree of the root

the number underneath the radical

nth root

for any real numbers "a" and "b", and any positive integer "n…

principal root

when a radical has two answers , the positive answer

composite function

index

inverse function

inverse relation

a function formed by evaluating one function with another fun…

the part of a radical that gives the degree of the root.

a function that "undoes" what the original function does. Swi…

the set or ordered pairs obtained by switching the x and y co…

composite function

a function formed by evaluating one function with another fun…

index

the part of a radical that gives the degree of the root.

consistent

dependent

elimination

inconsistent

When the graphs of a system of equations intersect or coincide.

A system of equations with an infinite number of solutions.

Solving systems of equations by adding the two equations toge…

A system of equations with no ordered pairs that satisfy the…

consistent

When the graphs of a system of equations intersect or coincide.

dependent

A system of equations with an infinite number of solutions.

Consistent

Dependent

Elimination Method

Inconsistent

a system of equations that has at least one ordered pair that…

a system of equations that has an infinite number of solutions

solving systems by adding or subtracting equations to elimina…

A system of equations that has no solutions

Consistent

a system of equations that has at least one ordered pair that…

Dependent

a system of equations that has an infinite number of solutions

Consistent

Dependent

Elimination

Inconsistent

a system of equations that has at least one ordered pair that…

a system of equations that has an infinite number of solutions.

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pairs that satisfy the…

Consistent

a system of equations that has at least one ordered pair that…

Dependent

a system of equations that has an infinite number of solutions.

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

a system of linear equations that has an infinite number of s…

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfies bot…

consistent

a system of linear equations that has at least one ordered pa…

dependent

a system of linear equations that has an infinite number of s…

axis of symmetry

parabola

square root property

completing the square

a line about which a figure is symmetric

the set of all points in plane that are the same distance fro…

for any real number n, if x squared = n, the x = plus or minu…

a process used to make a quadratic expression into a perfect…

axis of symmetry

a line about which a figure is symmetric

parabola

the set of all points in plane that are the same distance fro…

consistent

dependent

elimination method

inconsistent

a system of equations with at least one solution. [p. 365]

a consistent system with infinite solutions. [p. 365]

a way to solve a system of linear equations by adding or subt…

a system of equations with no solutions. [p. 365]

consistent

a system of equations with at least one solution. [p. 365]

dependent

a consistent system with infinite solutions. [p. 365]

Solve: 2n+6<4

Solve: 5n-4>11

Solve: 2x+5<6

If the inequality is 2<x, which way do…

n<-1 ... Graph: open circle at -1, shade to the left

n>3... Graph: open circle at 3, shade to the right

x<1/2 or x<0.5

Towards the larger numbers (right)

Solve: 2n+6<4

n<-1 ... Graph: open circle at -1, shade to the left

Solve: 5n-4>11

n>3... Graph: open circle at 3, shade to the right

composite function

index

inverse function

inverse relation

a function formed by evaluating one function with another fun…

the part of a radical that gives the degree of the root.

a function that "undoes" what the original function does.

a relationship in which one variable decreases when another v…

composite function

a function formed by evaluating one function with another fun…

index

the part of a radical that gives the degree of the root.

Take the converse and negate it

Take the conditional and negate it

When the exterior angle is equal to th…

Assume the opposite... Prove its wrong... Si…

Contrapositive

Inverse

Exterior angle inequality theorem

List the steps of an indirect proof

Take the converse and negate it

Contrapositive

Take the conditional and negate it

Inverse

Compound Inequality-

Inequality-

Intersection-

Solution of an Inequality-

2 inequalities that are combined into one statement by the wo…

A statement that compares two expressions by using the signs:…

The intersection of the two sets is the set of all elements t…

A value or values that make the inequality true

Compound Inequality-

2 inequalities that are combined into one statement by the wo…

Inequality-

A statement that compares two expressions by using the signs:…

Linear System / System of Equations

Point of Intersection

Solving a system by GRAPHING

Solving a system by SUBSTITUTION

Two or more equations with the same variables 2x+ 3y = 2 ... 5x…

Always an ORDERED PAIR (x,y)

1. Put in slope-intercept form... 2. Graph BOTH... 3. Find where th…

Linear System / System of Equations

Two or more equations with the same variables 2x+ 3y = 2 ... 5x…

Point of Intersection

Always an ORDERED PAIR (x,y)

addition property of equality

equation

inequality

inverse operations

the property that states that if you add the same number to b…

an algebraic or numerical sentence that shows that two quanti…

a mathematical sentence that compares two expressions using t…

operations that undo each other; addition and subtraction are…

addition property of equality

the property that states that if you add the same number to b…

equation

an algebraic or numerical sentence that shows that two quanti…

Equation

Solution

Equivalent Equation

Subtraction Property of Equality

a mathematical sentence that contains an equals sign, stating…

a replacement value for the variable in an open sentence. A v…

two or more equations with the same solution

if you subtract the same number from each side of an equation…

Equation

a mathematical sentence that contains an equals sign, stating…

Solution

a replacement value for the variable in an open sentence. A v…

expression

equation

Operation Symbols

inequality

NOT a number sentence. NO relation symbol

a number sentence that DOES contain an equal sign

X, - , + , /

a number sentence that DOES have a relation symbol

expression

NOT a number sentence. NO relation symbol

equation

a number sentence that DOES contain an equal sign

composite function

inverse function

nth root

principal root

a combination of two functions such that the output from the…

a relation formed by reversing x and y in a function. [p. 405]

for any real numbers A and B, and any positive integer N, if…

the positive square root of a number. [p. 361]

composite function

a combination of two functions such that the output from the…

inverse function

a relation formed by reversing x and y in a function. [p. 405]

Graph of an inequality

Equivalent inequalities

Compound Inequality

Absolute value equation

set of points that represent all solutions of the inequality

inequalities that have same solution

consists of two separate inequalities joined by and or or

distance between a and 0 on the number line

Graph of an inequality

set of points that represent all solutions of the inequality

Equivalent inequalities

inequalities that have same solution

graph of a linear inequality in one va…

equivalent inequalities

compound inequality

linear inequality in x and y

The set of points on a number line that represents all soluti…

Inequalities that have the same solutions

Two or more inequalities that are connected by the words 'and…

An inequality that can be written in the form ax+b<c where a,…

graph of a linear inequality in one va…

The set of points on a number line that represents all soluti…

equivalent inequalities

Inequalities that have the same solutions