Given 36 + 2mx = 88 and x = 2, find the value of m.

Step-by-step solution

1. 1

   Decide which letter is the unknown. The equation contains two letters, but $x$ is given as $2$, so the only thing left to determine is $m$. Substituting the known value first is what turns a two-variable equation into an ordinary one-variable one.

2. 2

   Substitute $x=2$.

   $36+2m(2)=88$

   Both the $2$ from the coefficient and the $2$ from $x$ multiply the $m$ — they do not add.

3. 3

   Simplify the $m$ term.

   $2m\cdot 2=4m\quad\Rightarrow\quad 36+4m=88$

4. 4

   Undo the addition. Subtract $36$ from both sides:

   $4m=88-36=52$

5. 5

   Divide by the coefficient and check.

   $m=\frac{52}{4}=13$

   Substituting back: $36+2(13)(2)=36+52=88$ ✓. So $m=13$.