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Warm Up

Practice solving absolute value equations and understand the concept in a warm-up session. Examples, guided practice, and solutions provided.

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Warm Up

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  1. Solve Absolute Value Equations Warm Up Lesson Presentation Lesson Quiz

  2. 1. Fora = –12, find, –a and |a|. ANSWER 12, 12 –2.5 ft ANSWER Evaluate |x|– 2 when x = –3. 2. 1 ANSWER Warm-Up The change in elevation as a diver explored a reef was –0.5 foot, 1.5 feet, –2.5 feet, and 2.25 feet. Which change in elevation had the greatest absolute value? 3.

  3. Solve x=7. ANSWER The solutions are 7 and –7. Example 1 SOLUTION The distance between x and 0 is 7. So, x =7or x =–7.

  4. ANSWER 3, –3 a. 15, –15 b. Guided Practice Solve (a) |x| = 3 and (b) |x| = 15.

  5. x – 3 = 8. Solve x – 3 = 8 ANSWER The solutions are 11 and –5. Check your solutions. Example 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. Write original equation. x – 3 = 8 or x – 3 = –8 Rewrite as two equations. x = 11 or x = –5 Add 3 to each side.

  6. ? ? |11– 3| = 8 |–5–3| = 8 ? ? | 8| = 8 |–8| = 8 8 = 8 8 = 8 Example 2 CHECK |x – 3| = 8 |x –3| = 8 Write original inequality. Substitute for x. Subtract. Simplify. The solution checks.

  7. Solve 32x – 7 – 5 = 4. First, rewrite the equation in the form ax + b = c. 32x – 7 – 5 = 4 32x – 7 = 9 2x – 7 = 3 Example 3 SOLUTION Write original equation. Add 5 to each side. Divide each side by 3.

  8. 2x – 7 = 3 ANSWER The solutions are 5 and 2. Example 3 Next, solve the absolute value equation. Write absolute value equation. 2x – 7 = 3 or2x – 7 = –3 Rewrite as two equations. 2x = 10 or2x = 4 Add 7 to each side. x = 5 or x = 2 Divide each side by 2.

  9. r – 7 = 9 3. 2. 2 s + 4.1 = 18.9 ANSWER 16, –2 ANSWER –3, –15 ANSWER 7.4, –7.4 4 t + 9 – 5 = 19 4. Guided Practice Solve the equation.

  10. Solve 3x + 5 + 6 = –2, if possible. 3x+5+6= –2 3x+5= –8 ANSWER The absolute value of a number is never negative. So, there are no solutions. Example 4 Write original equation. Subtract 6 from each side.

  11. 6. –3 n +2 –7 = –10 5. 2 m – 5 + 4 = 2 ANSWER 1, 3 no solution ANSWER Guided Practice Solve the equation, if possible

  12. Example 5 BASKETBALLS Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of 0.5 psi. (Absolute error is the absolute deviation of a measured value from an accepted value.) Find the minimum and maximum acceptable air pressures for the basketball.

  13. 0.5 = p – 8 Example 5 SOLUTION Let pbe the air pressure (in psi) of a basketball. Write a verbal model. Then write and solve an absolute value equation.

  14. or p p p 8.5 = 8 8 or – – p –0.5 = 0.5 = 7.5 = p – 8 0.5 = ANSWER The minimum and maximum acceptable pressures are 7.5 psi and 8.5 psi. Example 5 Write original equation. Rewrite as two equations. Add 8 to each side.

  15. ANSWER 12.8,2.4 Guided Practice 7. The absolute deviation of x from 7.6 is 5.2. What are the values of x that satisfy this requirement?

  16. ANSWER ANSWER –9, 17 –5, 11 ANSWER ANSWER no solutions no solutions Lesson Quiz Solve the equation, if possible. 1. | x – 4 | = 13 2. | x+ 2 | + 7 = 3 3. | 2x – 6 | + 4 = 20 4. –2 | x– 5 | + 7 = 12

  17. 5. A pattern for a 26-inch skirt for an absolute deviation of 1.5 inches. Find the minimum and maximum skirt lengths that can be made from the pattern. ANSWER minimum : 24.5 in.; maximum 27.5 in. Lesson Quiz

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