1 6 Solving Linear Inequalities Linear Inequality A

1. 6 Solving Linear Inequalities

Linear Inequality • A linear inequality is an equation but instead of an = there is an inequality sign. Ex: 2 x + 7 > 3 -3 – 6 x ≤ 12

Inequality Symbols Less than Greater than Less than or equal to Greater than or equal to Not equal to

Remember… • If you multiply or divide by a negative number, you MUST flip the inequality sign!

Solve the inequality. 2 x – 3 < 8

Graphing Linear Inequalities • Remember: < and > signs will have an open dot o and signs will have a closed dot graph of 4 5 6 graph of 7 -3 -2 -1 0

Solve the inequality. Then graph the solution. -8 x + 12 < -4

Solve the inequality. Then graph the solution. 41< 5 – 12 x -5 -4 -3 -2 -1 0 1 2

Solve the inequality. 3 x + 12 > 5 x -2

Compound Inequality • An inequality joined by “and” or “or”. Examples “and” “or” -4 -3 -2 -1 0 1 2 think between -3 -2 -1 0 1 2 3 4 think outside 5

Solve & graph. -6 x + 9 < 3 or -3 x - 8 > 13 Think outside -7 1

Solve & graph. 15 < -3 x - 6 and -3 x - 6 < 12 Think between!

Solve & graph. -9 < t+4 < 10 Think between! -13 6

Solve & graph. -6 < 4 t - 2 < 14

Absolute Value Equations and Inequalities

Absolute Value • Absolute value of a number is its distance from zero on a number line. 2 units -2 -1 0 1 2 3

Example Solve

Example Solve

Example Solve:

Example: Isolate the absolute value expression FIRST Solve

Example Solve

Solving Absolute Value Inequalities ● Step 1: Rewrite the inequality as a conjunction or a disjunction. ● If you have a you are working with a conjunction or an ‘and’ statement. Remember: “Less thand” ● If you have a you are working with a disjunction or an ‘or’ statement. Remember: “Greator” ● Step 2: In the second equation you must negate the right hand side and flip the inequality sign. ● Step 3: Solve as a compound inequality.

Example : Solve then graph |x -5|< 3

Example : Solve then graph |2 x + 1| > 7

Example: Solve then graph

Example: Solve then graph