Question

Solve. 

A. |y| = 7 

B. |x| + 2 = 11

C. 3|a| = 27

Answer 1

Absolute value equations :

When solving equations, that involve absolute values, there are two cases to consider.

Case 1: The expression inside the absolute value symbol is positive or zero.

Case 2 :  The expression inside the absolute value symbol is negative.

Symbols : For any real numbers a and b, if | a | = b and b ≥ 0, then a = b or a = - b.

• A. The equation is | y | = 7.

Case 1: If a = b, then y = 7.

Case 2 : If a = - b, then y = - 7.

The solution of y = 7 or y = - 7

Thus, the solution set is { - 7, 7}.

• B. The equation is | x | + 2 = 11.

Subtract 2 from each side.

| x | + 2 - 2 = 11 - 2

| x | = 9.

Case 1: If a = b, then x = 9.

Case 2 : If a = - b, then x = - 9.

The solution is x = 9 or x = - 9

Thus, the solution set is { - 9, 9}.

• C. The equation is 3| a | = 27.

Divide each side by 3.

3| a |/3 = 27/3

| a | = 9.

Case 1: If a = b, then a = 9.

Case 2 : If a = - b, then a = - 9.

The solution is a = 9 or a = - 9

Thus, the solution set is { - 9, 9}.