Section 2.7 Absolute Value Inequalities 137 130. Brielle: When solving an absolute value inequality of the form uXu < k, will the answer always be a single interval? Please explain. Correct each student’s errors, if any. 131. Solve u2x - 5u < 13. Ed’s work: u2x - 5u <13 2x - 5 < 13 or 2x - 5>-13 2x < 18 or 2x>-8 x < 9 or x>-4 132. Solve u4x + 1u + 2 ≥ 15. Monica’s work: u4x + 1u + 2 ≥ 15 4x + 1 + 2 ≥ 15 or 4x + 1 + 2≤-15 4x ≥ 12 or 4x≤-18 x ≥ 3 or x≤-4.5 Calculate It! Find the test points of the inequalities algebraically and then use a graphing calculator to solve the inequality. 133. u8x + 4u < 12 134. u7x + 3u < 10 135. u5x - 14u ≥ 14 136. u4x - 9u ≥ 9 Think About It! 137. Solve the inequality: ux + 5u > ux - 7u 138. Solve the inequality: u2x - 6u ≤ ux + 4u 139. Use test points to solve: ux - 3u > ux + 2u 140. Use test points to solve: u2x - 3u ≥ ux + 1u GROUP ACTIVITY The Mathematics of Controlling Waste Your employer has assigned you with the task of controlling waste in the cutting room for a wrapping paper manufacturer. The company wants to lose less than 1% of wrapping paper for each run of 2000 sheets of paper. The reported width of each piece of square wrapping paper is 1 yd. The absolute error of the cutting machines is 0.25 in. in all directions. Determine if the current machines are within the desired standards. (Recall from Section 2.6 that Eabs = ux - au, where x is the exact measure and a is the approximated value.) 1. Let x be the actual length of the cut wrapping paper. Write an absolute value inequality that shows that the absolute error of one side of the paper is within 0.25 in. 2. Solve the inequality from part 1. Interpret the meaning in the context of the problem. 3. What are the maximum and minimum values for the area of a cut sheet of wrapping paper? 4. What is the maximum error of the area of the cut paper? 5. If the cutter wastes the maximum amount of paper (as found in part 4) for each piece of paper in the run, how much total waste would there be? 6. How many sheets of wrapping paper does the cutter waste for a run of 2000 sheets of paper? 7. What percentage of waste does this represent? 8. What would you report to your employer?
hendricks_intermediate_algebra_1e_ch1_3
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