3 Ext Solving AbsoluteValue Inequalities Quiz Chapter 2

3 -Ext Solving Absolute-Value Inequalities Quiz Chapter 2 Ext. – Absolute Value Solve each equation. 1. 2. 3. Holt Algebra 1 4. Write and solve an absolute value equation that represents the two numbers x that are 2 units from 7 on a number line. Graph the solutions

3 -Ext Solving Absolute-Value Inequalities Learning Target Students will be able to: Solve Absolute value inequalities. Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities When an inequality contains an absolute-value expression, it can be written as a compound inequality. The inequality |x| < 5 describes all real numbers whose distance from 0 is less than 5 units. The solutions are all numbers between – 5 and 5, so |x|< 5 can be written as – 5 < x < 5, which is the compound inequality x > – 5 AND x < 5. Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 1 A: Solving Absolute-Value Inequalities Involving < Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 2 ≤ 6 Since 2 is added to |x|, subtract 2 from both sides to undo the addition. |x| + 2 ≤ 6 – 2 |x| ≤ 4 4 units – 5 – 4 – 3 – 2 – 1 4 units 0 1 2 3 4 5 Think, “The distance from x to 0 is less than or equal to 4 units. ” x ≥ – 4 AND x ≤ 4 Write as a compound inequality. – 4 ≤ x ≤ 4 Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 1 B: Solving Absolute-Value Inequalities Involving < Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 5 < – 4 Since 5 is subtracted from |x|, add 5 to both sides to undo the subtraction. |x| – 5 < – 4 +5 +5 |x| < 1 1 unit – 2 – 1 Think, “The distance from x to 0 is less than 1 unit. ” 1 unit 0 1 – 1 < x AND x < 1 – 1 < x < 1 Holt Algebra 1 2 x is between – 1 and 1. Write as a compound inequality.

3 -Ext Solving Absolute-Value Inequalities Example 1 C: Solving Absolute-Value Inequalities Involving < Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x + 4| – 1. 5 < 3. 5 +1. 5 Since 1. 5 is subtracted from |x + 4|, add 1. 5 to both sides to undo the subtraction. |x + 4| < 5 5 units – 5 – 4 – 3 – 2 – 1 5 units 0 1 2 3 4 5 x + 4 > – 5 AND x + 4 < 5 – 4 – 4 x > – 9 AND x <1 Holt Algebra 1 Think, “The distance from x to – 4 is less than 5 units. ” x + 4 is between – 5 and 5.

3 -Ext Solving Absolute-Value Inequalities Example 1 C Continued x > – 9 AND x < 1 Write as a compound inequality. – 10 – 8 – 6 – 4 – 2 0 – 9 < x < 1 Holt Algebra 1 2 4 6 8 10

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 1 a Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 12 < 15 Since 12 is added to |x|, subtract 12 from both sides to undo the addition. |x| + 12 < 15 – 12 |x| < 3 3 units – 5 – 4 – 3 – 2 – 1 0 1 x > – 3 AND x < 3 – 3 < x < 3 Holt Algebra 1 2 3 4 5 Think, “The distance from x to 0 is less than 3 units. ” x is between – 3 and 3. Write as a compound inequality.

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 1 b Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 6 < – 5 Since 6 is subtracted from |x|, add 6 to both sides to undo the subtraction. |x| – 6 < – 5 + 6 +6 |x| < 1 1 unit – 2 – 1 0 1 x > – 1 AND x < 1 – 1 < x < 1 Holt Algebra 1 2 Think, “The distance from x to 0 is less than 1 unit. ” x is between – 1 and 1. Write as a compound inequality.

3 -Ext Solving Absolute-Value Inequalities The inequality |x| > 5 describes all real numbers whose distance from 0 is greater than 5 units. The solutions are all numbers less than – 5 or greater than 5. The inequality |x| > 5 can be written as the compound inequality x < – 5 OR x > 5. Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 2 A: Solving Absolute-Value Inequalities Involving > Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 2 > 7 – 2 |x| Since 2 is added to |x|, subtract 2 from both sides to undo the addition. >5 5 units – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 x < – 5 OR x > 5 Write as a compound inequality. Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 2 B: Solving Absolute-Value Inequalities Involving > Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 12 ≥ – 8 + 12 +12 Since 12 is subtracted from |x|, add 12 to both sides to undo the subtraction. |x| ≥ 4 4 units – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 x ≤ – 4 OR x ≥ 4 Write as a compound inequality. Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 2 C: Solving Absolute-Value Inequalities Involving > Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x + 3| – 5 > 9 + 5 +5 |x + 3| > 14 14 units – 16 – 12 – 8 – 4 Since 5 is subtracted from |x + 3|, add 5 to both sides to undo the subtraction. 14 units 0 4 8 12 16 x + 3 < – 14 OR x + 3 > 14 Holt Algebra 1

3 -Ext Solving Absolute-Value Inequalities Example 2 C Continued x + 3 < – 14 OR x + 3 > 14 – 3 – 3 x < – 17 OR x Solve the two inequalities. > 11 – 17 – 24 – 20 Holt Algebra 1 – 16 – 12 11 – 8 – 4 0 4 8 12 16 Graph.

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 2 a Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 10 ≥ 12 – 10 |x| ≥ Since 10 is added to |x|, subtract 10 from both sides to undo the addition. 2 2 units – 5 – 4 – 3 – 2 – 1 0 1 x ≤ – 2 OR x ≥ 2 Holt Algebra 1 2 3 4 5 Write as a compound inequality.

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 2 b Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 7 > – 1 +7 +7 |x| > 6 Since 7 is subtracted from |x|, add 7 to both sides to undo the subtraction. 6 units – 10 – 8 – 6 – 4 – 2 6 units 0 2 4 x < – 6 OR x > 6 Holt Algebra 1 6 8 10 Write as a compound inequality.

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 2 c Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. Since is added to |x + 2 |, subtract from both sides to undo the addition. 3. 5 units – 5 – 4 – 3 – 2 – 1 3. 5 units 0 1 OR Holt Algebra 1 2 3 4 5

3 -Ext Solving Absolute-Value Inequalities Check It Out! Example 2 c Continued Solve the two inequalities. OR OR 1 – 10 – 8 – 6 – 4 – 2 Holt Algebra 1 0 2 4 6 8 10 Graph.

3 -Ext Solving Absolute-Value Inequalities Quiz Chapter 3 Extension – Solving Abs. Value Inequalities Solve each absolute-value inequality and graph the solutions. 1. 2. -2 0 2 -15 0 13 Write an absolute-value inequality for each graph. 3. -2 0 2 -3 0 3 4. Holt Algebra 1