Solve the equation 7x + 8 = 3x - 12.

Step-by-step solution

1. 1

   Gather the variable on one side. Subtract $3x$ from both sides; choosing the side with the larger coefficient keeps that coefficient positive:

   $7x-3x+8=-12\quad\Longrightarrow\quad 4x+8=-12$

2. 2

   Gather the constants on the other side. Subtract $8$:

   $4x=-12-8=-20$

3. 3

   Divide by the coefficient.

   $x=\frac{-20}{4}=-5$

4. 4

   Check both sides separately. Substituting $x=-5$:

   $\text{left}=7(-5)+8=-35+8=-27$
   $\text{right}=3(-5)-12=-15-12=-27$

   They agree $\checkmark$. Evaluating each side independently, rather than reusing your rearranged line, is what makes this a genuine check.