91Ó°ÊÓ

Solve and graph. Write the answer using both set-builder notation and interval notation. $$ |x-1|<3 $$

Solve and graph. Write the answer using both set-builder notation and interval notation. $$ |x-3|+2>7 $$

Waterfalls. In order for a waterfall to be classified as a classical waterfall, its height must be less than twice its crest width, and its crest width cannot exceed one-and-one-half times its height. The tallest waterfall in the world is about 3200 ft high. Let \(h\) represent a waterfall's height, in feet, and w the crest width, in feet. Write and graph a system of inequalities that represents all possible combinations of heights and crest widths of classical waterfalls.

Use a graphing calculator to graph each inequality. a) \(3 x+6 y>2\) b) \(x-5 y \leq 10\) c) \(13 x-25 y+10 \leq 0\) d) \(2 x+5 y>0\)

Explain why the inequality \(|x+5| \geq 2\) can be interpreted as "the number \(x\) is at least 2 units from \(-5 . "\)

Solve for x and y. Assume that a, b, c, d, and m are positive constants. $$ c(6 x-4)d $$