Question

Consider the equation 4x−2=−2(ax+3), with constant a. Which of the following statements is true about the solution to the equation?

There is no value of a for which the equation will have no solution.

If a=2, then there is no solution.

If a=0, then there is no solution.

If a=−2, then there is no solution.

Answer 1

If a= − 2, then there is no solution.

Explanation:

4x−2=−2(ax+3)

2) a=0 one solution

4x - 2 = - 2(0x + 3)

4x - 2 = -6

4x = - 4

x = -1

1) a =2 one solution

4x−2=−2(2x+3)

4x - 2 = - 4x -6

8x = -4

x = - 1/2

3) a = -2 no solution

4x−2=−2(-2x+3)

4x - 2 = 4x - 6

4x-4x= - 6+2

0 = - 4 , wrong, so no solution