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? (1 point)

A)Equation 1 and equation 2 have no solutions.
B)Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
C)The solutions to equation 1 are x = 3, -1.5, and equation 2 has no solution.
D)The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.

Answer 1

Answer: C.

Explanation:

First, notice eqn 2 asks for a positive number to add to 8 and get 2. Eliminate all choices which claim eqn 2 has a solution.

Second, to eliminate A, add 5 to both sides and notice the absolute value isn't being asked to be negative.

To check, verify

|4 × 3 − 3|− 5 = 4

|4 × (-1.5) − 3|− 5 = 4