Solve the equation 3x + 7 = 22.

Step-by-step solution

1. 1

   Identify the order in which $x$ was operated on. Reading $3x+7$ left to right, $x$ was first multiplied by $3$ and then had $7$ added. To isolate $x$ you undo those steps in the reverse order: subtract first, divide second.

2. 2

   Subtract $7$ from both sides. Whatever is done to one side must be done to the other to keep the equality:

   $3x+7-7=22-7\quad\Longrightarrow\quad 3x=15$

3. 3

   Divide both sides by $3$.

   $\frac{3x}{3}=\frac{15}{3}\quad\Longrightarrow\quad x=5$

4. 4

   Substitute back into the original equation. This is the only check that matters, because it uses the untouched equation rather than any of your intermediate lines:

   $3(5)+7=15+7=22\qquad\checkmark$