#### 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.

Compound Inequality

Inequality

Linear Inequality

Solution Set

Two inequalities joined with "and" or "or

A mathematical statement that has two expressions that are no…

An inequality in two variables that would graph a line and sh…

A set of solutions that can be an infinite number of solutions

Compound Inequality

Two inequalities joined with "and" or "or

Inequality

A mathematical statement that has two expressions that are no…

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…

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…

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

(-4,-2)

(-1/5,-2)

consistent, dependent, infinitely many…

consistent, independent, one solution

2x - 3y = -2... y - 3x = 10

-10x + y = 0... 5x + 3y = -7

Classify the system of equations. Give the number of solution…

Classify the system of equations. Give the number of solution…

(-4,-2)

2x - 3y = -2... y - 3x = 10

(-1/5,-2)

-10x + y = 0... 5x + 3y = -7

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.

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

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)

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…

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.

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.

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…

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:…

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…

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…

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…

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.

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

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

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.