1. Equations & Inequalities

In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

In Exercises 91–100, find all values of x satisfying the given conditions. y = |2 - 3x| and y = 13

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |4x - 3| = |4x - 5|

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|4 - (5/2)x| + 6 = 18

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 2|3x - 2| = 14

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2

Solve each equation in Exercises 96–102 by the method of your choice. -4|x+1| + 12 = 0

Solve the equations containing absolute value in Exercises 94–95. |2x+1| = 7