Question

solve for r.
$-\frac{3}{5} = r + \frac{1}{10}$
$r = \square$

Explanation:

Step1: Subtract $\frac{1}{10}$ from both sides

To solve for \( r \), we need to isolate it. So we subtract \(\frac{1}{10}\) from both sides of the equation \(-\frac{3}{5}=r + \frac{1}{10}\). This gives us \( r=-\frac{3}{5}-\frac{1}{10} \).

Step2: Find a common denominator

The common denominator of 5 and 10 is 10. We rewrite \(-\frac{3}{5}\) with a denominator of 10. Since \(\frac{3}{5}=\frac{3\times2}{5\times2}=\frac{6}{10}\), then \(-\frac{3}{5}=-\frac{6}{10}\). Now our equation becomes \( r = -\frac{6}{10}-\frac{1}{10} \).

Step3: Subtract the fractions

When subtracting fractions with the same denominator, we subtract the numerators. So \( -\frac{6}{10}-\frac{1}{10}=\frac{-6 - 1}{10}=\frac{-7}{10} \).

Answer:

\( r = -\frac{7}{10} \)