Solve for x: 25 = (200 + 200)/x.

Step-by-step solution

1. 1

   Simplify the numerator first. It has no unknown in it:

   $200+200=400\qquad\Longrightarrow\qquad 25=\frac{400}{x}$

2. 2

   Note the domain and read the meaning. Since $x$ is a denominator, $x\neq0$. The equation says $400$ divided into parts of size $25$ — so $x$ counts how many such parts there are, which must be a number in the low tens.

3. 3

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

   $25x=400$

   The unknown has moved out of the denominator, turning a rational equation into a one-step linear one.

4. 4

   Divide by 25.

   $x=\frac{400}{25}=16$

   Since $25\times4=100$, we get $25\times16=400$ ✓ — a clean whole number, unlike the sibling problems with decimal right-hand sides.

5. 5

   Verify by substitution. $\dfrac{200+200}{16}=\dfrac{400}{16}=25$ ✓, matching the left side exactly, and $16\neq0$ so the domain restriction is satisfied.