Question

PLEASE! 10 POINTS! For what number A does the equation 3Ax - 24 = 5x - 9 + x have no solutions for x?

Answer 1

Answer:

A = 2

Step-by-step explanation:

When there are no solutions for x, both sides x cancel leaving an equation with two distinct numbers equal to each other (e.g. 6 = 0). Therefore, we must find a number A for which that happens.

Lets first simplify the equation, 3Ax - 24 = 5x - 9 + x = 6x - 9.

We want to cancel out the 6x on both sides. This happens when the left side also has 6x, so 3Ax = 6x -> A = 2.

Testing out this works, we get:

6x - 24 = 6x - 9 -> -24 = -9 (which isn’t true)

We get no solutions, which is what we are looking for! Therefore, A = 2 must be our answer!

I hope this helps! :)