Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 35

Answer

$(7.5, 10.5]$ Refer to the attached image below for the graph.
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Work Step by Step

For easier work, get rid of the fractions by multiplying the LCD (which is 12) to each part to have: $\\12(\frac{1}{6}) \lt 12 \cdot \frac{2x-13}{12} \le 12(\frac{2}{3}) \\2 \lt 2x-13 \le 8$ Add 13 to each part to have: $\\2+13 \lt 2x-13+13 \le 8+13 \\15 \lt 2x \le 21$ Divide 2 to each part to have: $\\7.5 \lt x \le 10.5$ Thus, the solution is $(7.5, 10.5]$.
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