#### 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 sys…

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

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 sys…

Boundary

Compound Inequality

Inequality

Intersection

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

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 solutio…

Boundary

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

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 solutio…

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 solutio…

Solution of an inequality

Equivalent inequalities

Roster form

Set-builder notation

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

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 makes…

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 not…

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

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 not…

Addition Property of Inequality

Division Property of Inequality

Inequality

Multiplication Property of Inequality

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

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 m…

Addition Property of Inequality

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

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 n…

= 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 n…

system of linear equations

solution of the system of linear equati…

no solution

infinitely many solutions

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

The intersection point of the two lines

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

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 v…

solution of the system of linear equati…

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 solutions…

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

(-4,-2)

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

(-1/5,-2)

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

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 vari…

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

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)

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

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.

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.

Properties of Inequalities

Theorem 6-1 - The Exterior Angle Inequa…

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 than…

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 Inequa…

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

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 tw…

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 num…

Addition Property of Equality

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

Addition Property of Inequality

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

Inequalities

Signs of Inequalities

Types of Inequalities

Linear Inequality

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

< 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 f…

Inequalities

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

Signs of Inequalities

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

addition property of equality

Additive property of inequality

Coefficient

Division property of Equality

if you add the same number to each side of a equation, the sid…

if you add the same number to each side of a inequality, the i…

the numerical factor of a term that contains a variable

if you divide each side of an equation by the same nonzero num…

addition property of equality

if you add the same number to each side of a equation, the sid…

Additive property of inequality

if you add the same number to each side of a inequality, the i…

Compound Inequality-

Inequality-

Intersection-

Solution of an Inequality-

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

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

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

A value or values that make the inequality true

Compound Inequality-

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

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 than…

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 than…

Indirect Proof

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

composite function

index of a radical

inverse function

inverse relation

a function formed by evaluating one function with another func…

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 va…

composite function

a function formed by evaluating one function with another func…

index of a radical

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

The measure of an exterior angle of a t…

If one side of a triangle is longer tha…

If one angle of a triangle is larger th…

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 o…

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

The measure of an exterior angle of a t…

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

If one side of a triangle is longer tha…

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

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 tw…

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 num…

Addition Property of Equality

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

Addition Property of Inequality

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

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…

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

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.