# Solving Linear Inequalities and Compound Inequalities

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• Solving Linear Inequalitiesand Compound Inequalities

• Inequality Symbols is less thanis greater thanis less than or equal tois greater than or equal tois not equal to

• Linear InequalityCan be written in the form ax+b0, ax+b0, or ax+b0 where a and b are real numbers and a0Has one variable to the first power.for example: 2x-3
• Transformations for InequalitiesAdd/subtract the same number on each side of an inequality

Multiply/divide by the same positive number on each side of an inequality

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

• Ex: Solve the inequality.2x-3
• Graphing Linear InequalitiesRemember: < and > signs will have an open circle and signs will have a closed circle

graph of graph of 4567-3-2-10

• Example: Solve and graph the solution.6789

• Example: Solve and graph the solution.This is a true statement, therefore the solution is ALL REAL NUMBERS.

• Compound InequalityAn inequality joined by and or or.Examples and/intersection or/union

think between think oars on a boat -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 3 4 5

• Example: Solve & graph.-9 < t+4 < 10-4 -4 -4-13 < t < 6

Think between!-136

• Solve & graph. -6x+9 < 3 or -3x-8 > 13 -6x < -6 -3x > 21 x > 1 or x < -7

Flip signsThink oars-71

• Assignmentp.45-46 #12-33 m3, 42, 48, 51, 53, 56

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