Section 1.6 Absolute Value Equations 99 a 0, 0x 0 a, a 6 0, x a or x a. Solving an Absolute Value Equation Solve the equation. Solution: The equation is already in the form Rewrite as two equations. Solve each equation. 2w 3 5 or 2w 3 5 2w 8 or 2w 2 w 4 or w 1 Check: w 4 Check: w 1 Check the values in the original 2w 3 0 5 0 2w 3 0 5 0 2 112 3 0 5 0 2 142 3 0 5 0 2 3 0 5 0 8 3 0 5 0 5 0 5 0 5 0 5 0 ✔ ✔ 54, 16 The solution set is . Skill Practice Solve the equation. 5. Solving an Absolute Value Equation 04x 1 0 9 Example 3 Solve the equation. Solution: 02c 5 0 6 2 Isolate the absolute value. The equation is in the form where Because there is no solution. 02c 5 0 6 2 02c 5 0 4 5 6 0x 0 x 2c 5 and a 4. a, a 6 0, No solution, There are no numbers c that will make an absolute value equal to a negative number. Skill Practice Solve the equation. 6. 03z 10 0 3 1 0x 0 a, where x 2w 3. 02w 3 0 5 02w 3 0 5 Example 2 equation. Avoiding Mistakes Always isolate the absolute value first. Otherwise you will get answers that do not check. Answers 5. e 2, 6. No solution, 5 6 5 2 f Solving an Absolute Value Equation Step 1 Isolate the absolute value.That is, write the equation in the form where a is a real number. Step 2 If there is no solution. Step 3 Otherwise, if rewrite the absolute value equation as Step 4 Solve the individual equations from step 3. Step 5 Check the answers in the original absolute value equation.
miller_intermediate_algebra_4e_ch1_3
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