1.6 Solving Linear Inequalities

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

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

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

Solve the inequality. 2x – 3 < 8

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

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

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

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

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

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

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

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

Solve & graph. -6 < 4t - 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 2 1 -1 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

Example : Solve then graph

Example: Solve then graph

Example: Solve then graph