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Inequalities: Graphing and Solving with Examples

Learn how to graph and solve inequalities with examples and guided practice exercises for mastering the concepts.

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Inequalities: Graphing and Solving with Examples

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  1. 1 All numbers greater than or equal to 2 d. h 2 1 2 2 EXAMPLE 1 Graphing Inequalities Inequality Graph Verbal Phrase a.y< 7 All numbers less than 7 All numbers less than or equal to 3 b. q 3 c. x > –5 All numbers greater than –5

  2. x – 5 < 8 a. EXAMPLE 2 Solving Inequalities Solve the inequality. Then graph its solution. x – 5 < 8 Original inequality x – 5 + 5< 8 + 5 Add 5 to each side. x < 13 Simplify.

  3. EXAMPLE 2 Solving Inequalities b. y – 7  –10 y – 7  –10 Original inequality y – 7 + 7– 10 + 7 Add 7 to each side. y  –3 Simplify.

  4. EXAMPLE 2 Solving Inequalities c. 8+ m > 15 8+ m > 15 Original inequality 8 – 8+ m >15 – 8 Subtract 8 from each side. m > 7 Simplify.

  5. –3 –2 –1 0 1 for Examples 1 and 2 GUIDED PRACTICE Graph and write a verbal phrase for the inequality. 1. z ≥ –1 SOLUTION Inequality Graph Verbal Phrase All numbers greater than or equal to –1 z ≥ –1

  6. 2 3 4 5 6 for Examples 1 and 2 GUIDED PRACTICE 2. 4> p SOLUTION Inequality Graph Verbal Phrase 4> p All numbers less than 4.

  7. –5 –4 –3 –2 –1 for Examples 1 and 2 GUIDED PRACTICE 3. k  –3.5 SOLUTION Inequality Graph Verbal Phrase k  –3.5 All numbers less than or equal to –3.5.

  8. 1 4. m > 2 1 1 All numbers greater than . m > –2 –1 0 1 2 2 2 for Examples 1 and 2 GUIDED PRACTICE SOLUTION Inequality Graph Verbal Phrase

  9. + 3 – 2 + 3 x – 3 x  1 Graph for Examples 1 and 2 GUIDED PRACTICE 5.x – 3 > –2 SOLUTION x – 3 > – 2 Original inequality Add 3 to each side. Simplify.

  10. 6 + 1 > t – 1 + 1 7 > t Graph for Examples 1 and 2 GUIDED PRACTICE 6. 6 > t – 1 SOLUTION 6 > t – 1 Original inequality Add 1 to each side. Simplify.

  11. 12 ≥ p + 14 – 14 – 14 ≥ p –2 Graph for Examples 1 and 2 GUIDED PRACTICE 7. 12 ≥ p + 14 SOLUTION 12 ≥ p + 14 Original inequality Subtract 14 from each side. Simplify.

  12. – 5 –5 x + 5 < 10 x < 5 3 4 5 6 7 x< 5 Graph for Examples 1 and 2 GUIDED PRACTICE 8.x + 5 < 10 SOLUTION x + 5 < 10 Original inequality Subtract 5 from each side. Simplify.

  13.  6 t + 9 – 9 – 9 –3 t  Graph for Examples 1 and 2 GUIDED PRACTICE 9.t + 9  6 SOLUTION t + 9  6 Original inequality Subtract 9 from each side. Simplify.

  14. –4 + 3 < k – 3 + 3 –1 < k Graph for Examples 1 and 2 GUIDED PRACTICE 10. –4 < k –3 SOLUTION –4 < k– 3 Original inequality Subtract 9 from each side. Simplify.

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