Solve for x: 14 = (108 + 84)/x.

Step-by-step solution

1. 1

   Simplify the numerator first. It contains no unknown:

   $108+84=192\qquad\Longrightarrow\qquad 14=\frac{192}{x}$

   The domain restriction is $x\neq0$.

2. 2

   Estimate before solving. The equation asks how many parts of size $14$ fit into $192$. Since $14\times14=196$ is slightly more than $192$, expect $x$ a little under $14$.

3. 3

   Clear the denominator. Multiply both sides by $x$:

   $14x=192$

4. 4

   Divide by 14.

   $x=\frac{192}{14}$

5. 5

   Reduce to lowest terms. Both $192$ and $14$ are even, so divide by $2$:

   $\frac{192}{14}=\frac{96}{7}$

   Since $7$ is prime and does not divide $96$, this is fully reduced. As a decimal, $\tfrac{96}{7}=13.\overline{714285}\approx13.714$ — just under $14$, as predicted ✓.

6. 6

   Verify with exact arithmetic. $\dfrac{192}{96/7}=192\times\dfrac{7}{96}=\dfrac{1344}{96}=14$ ✓, matching the left side exactly.