Question

The table below shows two equations:

Equation 1: |2x − 3| + 5 = 4 Equation 2: |5x + 3| − 10 = 3.
Which statement is true about the solution to the two equations?
A.Equation 1 and equation 2 have no solutions.
B.Equation 1 has no solution and equation 2 has solutions x = 2, −3.2.
C.The solutions to equation 1 are x = 1, 2 and equation 2 has no solution.
D.The solutions to equation 1 are x = 1, 2 and equation 2 has solutions x = 2, −3.2.

Answer 1

Equation 1

Subtracting 5 from both sides we have

|2x - 3| = -1 - Since an absolute values must be positive this equation has no solutions.

Equation 2:-

|5x + 3| - 10 = 3

|5x + 3| = 13

either 5x + 3 = 13 or 5x + 3 = -13

so x = 2 or x = -16/5 = -3.2

The correct choice is B