Question

Solve 8x + 9 = 3(x - 1) + 7.

Answer 1

The equation is 8x + 9 = 3x - 3 + 7 = 3x + 4.
By transposing, we get 8x - 3x = 4 - 9
or
5x = - 5.
We thus get x = - 1.
We can verify this:
8x + 9 = 8(-1) + 9 = - 8 + 9 = 1
and
3(x - 1) + 7 = 3(-1-1) + 7 = 3(-2) + 7 = - 6 + 7 = 1.
Thus 8x + 9 = 3(x - 1) + 7 is true for x = - 1.
This checks that x = - 1 is a solution.