Question

(25 POINTS!!) This absolute value equation has bested absolute values. Use your knowledge of solving absolute value equations to solve this equation. Justify the number of possible solutions.

Answer 1

x = 4

Explanation:

Break down the problem into these 2 equations.

(2x + 5) -3 = 10

-(-(2x + 5) -3) = 10

Solve the 1st equation: (2x + 5) -3 = 10

x=4

Solve the 2nd equation: -(-(2x + 5) -3) = 10

x = 1

Collect all solutions.

x = 1, 4

Check solution

When x = 1, the original equation ||2x + 5| -3| = 10∣does not hold true.

We will drop x = 1 from the solution set.

Therefore,

x = 4