Question

24. Justify Your Reasoning This absolute value equation has nested absolute values.

Use your knowledge of solving absolute value equations to solve this equation. Justify
the number of possible solutions.
||2x + 5|—3|= 10

Answer 1

The equation can be solved by breaking it down into two separate absolute value equations:

||2x + 5|= 13 and |—3|= 10.

The first equation has two possible solutions: x = 4 or x = -8.

The second equation has one possible solution: -3 = 10.

Since both equations must be true for the original equation to be true, there is only one possible solution to the original equation: x = 4.

Therefore, the original equation has one possible solution.