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# 1.6 solving linear inequalities

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### 1.6 solving linear inequalities

1. 1. Solving Linear Inequalities
2. 2. Inequality SymbolsInequality Symbols ≠≥≤>< Less than Greater than Less than or equal to Greater than or equal to Not equal to
3. 3. Linear Inequality • Inequality with one variable to the first power. for example: 2x-3<8 • A solution is a value of the variable that makes the inequality true. x could equal -3, 0, 1, etc.
4. 4. Transformations for InequalitiesTransformations for Inequalities • Add/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!
5. 5. Ex: Solve the inequality. 2x-3<8 +3 +3 2x<11 2 2 x< 2 11 1373 ≤+− x 63 ≤− x 2−≥x Flip the sign after dividing by the -3!
6. 6. Graphing Linear Inequalities • Remember: < and > signs will have an open dot o and signs will have a closed dot graph of graph of ≤ ≥ 2 11 <x 2−≥x • 4 5 6 7 -3 -2 -1 0
7. 7. Example: Solve and graph the solution. 121097 −≥+ xx 1239 −≥ x x321≥ x≥7 6 7 8 9
8. 8. Compound Inequality • An inequality joined by “and” or “or”. Examples “and” “or” think between think oars on a boat 13 ≤<− x -4 -3 -2 -1 0 1 2 4or2 >−≤ xx -3 -2 -1 0 1 2 3 4 5
9. 9. Example: Solve & graph. -9 < t+4 < 10 -13 < t < 6 Think between! -13 6
10. 10. Last example! Solve & graph. -6x+9 < 3 or -3x-8 > 13 -6x < -6 -3x > 21 x > 1 or x < -7 Flip signs Think oars -7 1