23. Solve |4x - 11| < 5. You must show all work. Use complete sentences to describe the graph in words.
One non-graphical way (easier to explain here) is to say that
(4x - 11)² < 25 (Squaring removes any issues with negative signs)
16x² - 88x +121 < 25
16x² - 88x + 96 < 0
2x² - 11x + 12 < 0
(x - 4)(2x - 3) < 0
3/2 < x < 4
The graph of |4x - 11| is v-shaped and the vertex of the v meets the x axis at x = 11/4.
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Answers & Comments
One non-graphical way (easier to explain here) is to say that
(4x - 11)² < 25 (Squaring removes any issues with negative signs)
16x² - 88x +121 < 25
16x² - 88x + 96 < 0
2x² - 11x + 12 < 0
(x - 4)(2x - 3) < 0
3/2 < x < 4
The graph of |4x - 11| is v-shaped and the vertex of the v meets the x axis at x = 11/4.