Question

complete the steps to solve for x.
\\(\frac{3}{5}x - \frac{1}{4}x = 7\\)
\\(\frac{3}{5}x - \frac{1}{4}x = 7\\)
\\(\frac{square}{20}x = 7\\)

Explanation:

Step1: Find common denominator

The common denominator of 5 and 4 is 20. Rewrite the fractions: $\frac{3}{5}x = \frac{12}{20}x$ and $\frac{1}{4}x = \frac{5}{20}x$.

Step2: Subtract the fractions

Subtract the two fractions: $\frac{12}{20}x - \frac{5}{20}x = \frac{7}{20}x$. So the box should be filled with 7. Then, to solve for x, multiply both sides by $\frac{20}{7}$: $x = 7\times\frac{20}{7} = 20$. But for the first box (the numerator in the fraction over 20), we found it's 7.

Answer:

The number in the box is 7, and the solution for \( x \) is \( 20 \). (For the box in the given equation, the answer is 7.)