1. Equations & Inequalities

Write each statement using an absolute value equation or inequality. r is no less than 1 unit from 29.

Write each statement using an absolute value equation or inequality. q is no more than 8 units from 22.

In Exercises 59–94, solve each absolute value inequality.|(2x + 2)/4| ≥ 2

In Exercises 59–94, solve each absolute value inequality.|3 - (2/3)x| > 5

The temperatures on the surface of Mars in degrees Celsiusapproximately satisfy the inequality |C + 84 | ≤ 6. What range of temperaturescorresponds to this inequality?

In Exercises 59–94, solve each absolute value inequality.3|x - 1| + 2 ≥ 8

In Exercises 59–94, solve each absolute value inequality.5|2x + 1| - 3 ≥ 9

In Exercises 59–94, solve each absolute value inequality.- 2|x - 4| ≥ - 4

In Exercises 59–94, solve each absolute value inequality.- 4|1 - x| < - 16

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x | = 6, work Exercises 83–86 in order. For x^2 - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

Solve each inequality. Give the solution set using interval notation. 11x≥2(x-4)

In Exercises 59–94, solve each absolute value inequality.3 ≤ |2x - 1|

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

Solve each inequality. Give the solution set using interval notation. 7x-2(x-3) ≤5(2-x)

Use the method described in Exercises 83–86, if applicable, and properties ofabsolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 canbe solved by inspection.) | 3x^2 + x | = 14