The equation 8 (3x - 2) - 4 = 8x + 4 (4x - 3) has what type of solution set?

Infinite

Two-solution

One-solution

No solution

Answer: D. No solution

Let's solve for x

8 (3x-2) - 4 = 8x + 4 (4x-3)

8 (3x) + 8 (-2) - 4 = 8x+4 (4x) + 4 (-3)

24x-16-4 = 8x+16x-12

24x-20 = 24x-12

-20 = - 12 ... subtract 24x from both sides, the two terms cancel each other out

We end up with a false equation as both sides are not the same number.

No matter what value of x you plug in, you'll get a false equation.

This is known as a contradiction because the left hand side says one thing, but the right hand side says something else.