Solve for x: (148 + 200)/x = 0.05.

Step-by-step solution

1. 1

   Simplify the numerator before anything else. The sum is a fixed number, so collapse it first:

   $148+200=348\qquad\Longrightarrow\qquad \frac{348}{x}=0.05$

   This turns a two-step problem into a single proportion.

2. 2

   Note the domain restriction. The unknown sits in the denominator, so $x\neq0$. Any answer must be checked against this — here the final value is far from zero, so the restriction is harmless, but stating it is part of solving a rational equation correctly.

3. 3

   Clear the denominator by multiplying both sides by x.

   $348=0.05x$

   Equivalently, the original equation says "$x$ goes into $348$ exactly $0.05$ times per unit", so $x$ must be much larger than $348$ — a useful size check before computing.

4. 4

   Divide by 0.05, using the reciprocal shortcut. Because $\dfrac{1}{0.05}=\dfrac{1}{\frac{1}{20}}=20$, dividing by $0.05$ is the same as multiplying by $20$:

   $x=\frac{348}{0.05}=348\times20=6960$

5. 5

   Verify by substituting back. $\dfrac{148+200}{6960}=\dfrac{348}{6960}=0.05$ exactly, since $348\times20=6960$ ✓. The result is indeed much larger than $348$, matching the size estimate.