Question

The table below shows two equations:

Equation 1: |4x - 3|- 5 = 4
Equation 2: |2x + 3| + 8 = 3


Which statement is true about the solution to the two equations?
Equation 1 and equation 2 have no solutions.

Equation 1 has no solution and equation 2 has solutions x = -4, 1.

The solutions to equation 1 are x = 3, -1.5 and equation 2 has no solution.

The solutions to equation 1 are x = 3, -1.5 and equation 2 has solutions x = -4, 1.

Answer 1

This problem can be solved by using the answer choices. We plug in the given values of the equations and see if they satisfy it.
| 4(3) - 3 | - 5 = 4
4 = 4; this is a solution
| 4(-1.5) - 3 | - 5 = 4
4 = 4; this is a solution

|2(-4) + 3| + 8 = 3
13 =/= 3, not a solution

|2(1) + 3| + 8 = 3
13 =/= 3, not a solution

Thus, equation 1 has two solutions, x = 3 and x = -1.5, while equation 2 has no solutions. The third option is correct.