Solve a compound inequality with and

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Solve a compound inequality with and EXAMPLE 4 Solve a compound inequality with and Solve –5  –x – 3  2. Graph your solution. –5  –x – 3  2 Write original inequality. –5 + 3  –x – 3 + 3  2 + 3 Add 3 to each expression. –2  –x  5 Simplify. –1(–2)  –1(–x)  –1(5) Multiply each expression by –1 and reverse both inequality symbols. 2  x  –5 Simplify.

Solve a compound inequality with and EXAMPLE 4 Solve a compound inequality with and –5  x  2 Rewrite in the form a  x  b. ANSWER The solutions are all real numbers greater than or equal to –5 and less than or equal to 2.

Solve a compound inequality with or EXAMPLE 5 Solve a compound inequality with or Solve 2x + 3 < 9 or 3x – 6 > 12. Graph your solution. SOLUTION Solve the two inequalities separately. 2x + 3 < 9 or 3x – 6 > 12 Write original inequality. 2x + 3 – 3 < 9 – 3 or 3x – 6 + 6 > 12 + 6 Addition or Subtraction property of inequality 2x < 6 or 3x > 18 Simplify.

Solve a compound inequality with or EXAMPLE 5 Solve a compound inequality with or 2x 2 6 < or 3x 3 18 > Division property of inequality x < 3 or x > 6 Simplify. ANSWER The solutions are all real numbers less than 3 or greater than 6.

GUIDED PRACTICE for Examples 4 and 5 Solve the inequality. Graph your solution. 7. –14 < x – 8 < –1 –6 < x < 7 ANSWER

GUIDED PRACTICE for Examples 4 and 5 Solve the inequality. Graph your solution. 8. –1  –5t + 2  4 –  t  2 5 3 ANSWER

GUIDED PRACTICE for Examples 4 and 5 Solve the inequality. Graph your solution. 9. 3h + 1< – 5 or 2h – 5 > 7 h < –2 or h > 6 ANSWER

GUIDED PRACTICE for Examples 4 and 5 Solve the inequality. Graph your solution. 10. 4c + 1  –3 or 5c – 3 > 17 c  –1 or c > 4 ANSWER