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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities 3-Ext Solving Absolute-Value Inequalities Holt Algebra 1 Lesson Presentation Lesson Presentation

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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 AND x < 5.

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Example 1A: Solving Absolute-Value Inequalities Involving < Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| + 2 6 –2 |x| 4 x –4 AND x 4 –5 –4 –3–2 –1 012345 4 units –4 x 4 Since 2 is added to |x|, subtract 2 from both sides to undo the addition. Think, The distance from x to 0 is less than or equal to 4 units. Write as a compound inequality.

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities |x| – 5 < –4 +5 |x| < 1 –1 < x AND x < 1 –1 < x < 1 Since 5 is subtracted from |x|, add 5 to both sides to undo the subtraction. Think, The distance from x to 0 is less than 1unit. x is between –1 and 1. Write as a compound inequality. –2 –1 012 unit 1 1 Example 1B: Solving Absolute-Value Inequalities Involving < Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities |x + 4| – 1.5 < 3.5 +1.5 |x + 4| < 5 Since 1.5 is subtracted from |x + 4|, add 1.5 to both sides to undo the subtraction. Think, The distance from x to –4 is less than 5 units. x + 4 > –5 AND x + 4 < 5 x + 4 is between –5 and 5. –5 –4 –3–2 –1 012345 Example 1C: Solving Absolute-Value Inequalities Involving < –4 –4 x > –9 AND x < 1 Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. 5 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities x > –9 AND x < 1 –9 < x < 1 –10 –8 –6–4 –2 0246810 Write as a compound inequality. Example 1C Continued

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 1a |x| + 12 < 15 – 12 –12 |x| < 3 Since 12 is added to |x|, subtract 12 from both sides to undo the addition. Think, The distance from x to 0 is less than 3 units. x is between –3 and 3. x > –3 AND x < 3 –3 < x < 3 Write as a compound inequality. Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. –5 –4 –3–2 –1 012345 3 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 1b |x| – 6 < –5 + 6 +6 |x| < 1 Since 6 is subtracted from |x|, add 6 to both sides to undo the subtraction. Think, The distance from x to 0 is less than 1 unit. –2 –1 012 x > –1 AND x < 1 –1 < x < 1 x is between –1 and 1. Write as a compound inequality. Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. 1 unit

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Holt Algebra 1 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.

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. Example 2A: Solving Absolute-Value Inequalities Involving > |x| + 2 > 7 – 2 –2 |x| > 5 x 5 Since 2 is added to |x|, subtract 2 from both sides to undo the addition. Write as a compound inequality. –10 –8 –6–4 –2 0246810 5 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. |x| – 12 –8 + 12 +12 |x| 4 –10 –8 –6–4 –2 0246810 x –4 OR x 4 Since 12 is subtracted from |x|, add 12 to both sides to undo the subtraction. Write as a compound inequality. Example 2B: Solving Absolute-Value Inequalities Involving > 4 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. Example 2C: Solving Absolute-Value Inequalities Involving > |x + 3| – 5 > 9 + 5 +5 |x + 3| > 14 Since 5 is subtracted from |x + 3|, add 5 to both sides to undo the subtraction. –16 –12 –8–404 81216 x + 3 14 14 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities – 3 –3 –3 –3 x 11 Solve the two inequalities. –24 –20 –16–12 –8 –40481216 –17 11 Graph. Example 2C Continued x + 3 14

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 2a |x| + 10 12 – 10 –10 |x| 2 –5 –4 –3–2 –1 012345 x –2 OR x 2 Write as a compound inequality. Since 10 is added to |x|, subtract 10 from both sides to undo the addition. Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. 2 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 2b |x| – 7 > –1 +7 |x| > 6 –10 –8 –6–4 –2 0246810 x 6 Since 7 is subtracted from |x|, add 7 to both sides to undo the subtraction. Write as a compound inequality. Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. 6 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 2c –5 –4 –3–2 –1 012345 Since is added to |x + 2 |, subtract from both sides to undo the addition. OR Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. 3.5 units

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Holt Algebra 1 3-Ext Solving Absolute-Value Inequalities Check It Out! Example 2c Continued OR –10 –8 –6–4 –2 0246810 1 Solve the two inequalities. Graph.

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