Question

Solve the equations. (a) |x|=2 (b) |x|=0 (c) |x|=-2 If there is more than one solution, separate the answers with commas. The solution set of |x|=2 is

Answer 1

The equations |x| = 2, |x| = 0, and |x| = -2 have solutions x = 2, x = -2; x = 0; and no solution respectively. The solution set for |x| = 2 is x = 2 and x = -2.

Step-by-step explanation:

The task is to solve the following absolute value equations:

1. |x| = 2
2. |x| = 0
3. |x| = -2

(a) |x| = 2: An absolute value equation is true when the expression inside the absolute value is equal to the number on the other side of the equation or its opposite. Therefore, x can be 2 or -2, which gives us two solutions: x = 2, x = -2.

(b) |x| = 0: The only number whose absolute value is 0 is 0 itself. Hence, the solution is x = 0.

(c) |x| = -2: An absolute value can never be negative, because it represents the distance from 0 on the number line. As such, this equation has no solution.

For the solution set of |x| = 2, we have two possible solutions x = 2 and x = -2.