Graph Inequalities on a Number Line

SWBAT use a replacement set to identify the solution set of an inequality; graph the solution set of an inequality on a number line; write an inequality that describes a given graph

Definitions Replacement set

A set of numbers to be used as possible values for the variable in an equation or inequality

Solution set Contains all the values for the variable

that make the equation or inequality true Empty set

A solution set that contains none of the numbers from the replacement set

Examples

Inequality Replacement set Solution set

y < 25 {24, 25, 26, …}

x > 8 {0, 1, 2, 3, …}

x ≤ 8 {4, 5, 6, 7, …}

t ≥ 10 {-3, -2, -1, 0, 1, 2, …}

t ≤ 10 {…, 8, 9, 10}

a < 0 {0, 1, 2, 3, …}

{24}

{9, 10, 11, 12, …}

{4, 5, 6, 7, 8}

{10, 11, 12, 13, …}

{…8, 9, 10,}

{}

Definitions Equivalent inequalities

Inequalities that have the same solution set

Graphing inequalities the number is NOT included in

solution set, use with < or >

the number IS included in the solution set, use with ≤ or

≥

Examples

x > 4 9 ≤ x x ≤ 0 2> x

Try the problems on your sheet

0 5 10 15-5

Anwers S={10, 12} S={14, 15, 16, 17} S={-1, 0, 1, 2, 3} S={10, 20, 30, 40, …}

x ≥ -1 x < 4 x > -9