Solve for x: -9x - 34 + 72 - 42 = -8x + 68 - 4x.

Step-by-step solution

1. 1

   Simplify each side separately before moving anything across. Six terms are scattered over two sides, and crossing the equals sign too early is what produces sign errors. Tidy each side into the form (coefficient)$\,x\,$ + (constant) first; only then start transposing.

2. 2

   Collect the constants on the left. The left side has one $x$ term and three numbers:

   $-34+72-42=38-42=-4$

   so the left side becomes

   $-9x-4$

3. 3

   Collect the $x$ terms on the right. The right side has two $x$ terms and one number:

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

   so the right side becomes

   $-12x+68$

   The equation is now the compact

   $-9x-4=-12x+68$

4. 4

   Gather $x$ on one side and numbers on the other. Add $12x$ to both sides and add $4$ to both sides:

   $-9x+12x=68+4\ \Longrightarrow\ 3x=72$

   Adding $12x$ (rather than subtracting $9x$) keeps the $x$ coefficient positive, which avoids a needless division by a negative later.

5. 5

   Divide and check by substitution. Dividing both sides by $3$:

   $x=\frac{72}{3}=24$

   Substituting $x=24$ back into the original equation, the left side is $-9(24)-34+72-42=-216-4=-220$ and the right side is $-8(24)+68-4(24)=-192+68-96=-220$. Both sides equal $-220$ exactly, so $x=24$ is the solution.