Solve for x: (158 + 159)/x = 7.8.

Step-by-step solution

1. 1

   Collapse the numerator first. It contains no unknown, so evaluate it immediately:

   $158+159=317\qquad\Longrightarrow\qquad \frac{317}{x}=7.8$

2. 2

   State the domain restriction. Because $x$ is a denominator, $x\neq0$. The final value must be checked against this.

3. 3

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

   $317=7.8x$

   Read as a rate, the equation says $317$ split into parts of size $7.8$ each — so $x$ counts how many such parts fit, and must be roughly $317/8\approx40$.

4. 4

   Divide by 7.8.

   $x=\frac{317}{7.8}=\frac{3170}{78}=\frac{1585}{39}$

   Multiplying numerator and denominator by $10$ clears the decimal; dividing by the common factor $2$ gives the reduced fraction $\tfrac{1585}{39}$.

5. 5

   Convert to a decimal.

   $\frac{1585}{39}=40.6410256\ldots\approx40.64$

   Since $39=3\times13$ has prime factors other than $2$ and $5$, the decimal repeats forever rather than terminating — the exact fraction is the cleaner answer.

6. 6

   Verify by substitution. $\dfrac{317}{40.6410256}=7.800000$ ✓, and the value is close to the estimate of about $40$ from step 3 ✓.