Question

Solve the equation for x.
three tenths x minus one fifth equals negative 2

Answer 1

To solve the equation \( \frac{3}{10} x - \frac{1}{5} = -2 \), follow these steps:

1. First, eliminate the fraction by finding a common denominator. The common denominator for 10 and 5 is 10. Rewrite the equation:
\[
\frac{3}{10} x - \frac{2}{10} = -2
\]

2. Now, add \( \frac{2}{10} \) to both sides of the equation:
\[
\frac{3}{10} x = -2 + \frac{2}{10}
\]
To compute \(-2 + \frac{2}{10}\), convert \(-2\) to a fraction with a denominator of 10:
\[
-2 = -\frac{20}{10}
\]
Therefore,
\[
-2 + \frac{2}{10} = -\frac{20}{10} + \frac{2}{10} = -\frac{18}{10} = -\frac{9}{5}
\]

3. Now the equation looks like this:
\[
\frac{3}{10} x = -\frac{9}{5}
\]

4. To isolate \( x \), multiply both sides by the reciprocal of \( \frac{3}{10} \) (which is \( \frac{10}{3} \)):
\[
x = -\frac{9}{5} \cdot \frac{10}{3}
\]

5. Multiply the fractions:
\[
x = -\frac{9 \cdot 10}{5 \cdot 3} = -\frac{90}{15}
\]

6. Simplify \( -\frac{90}{15} \):
\[
x = -6
\]

Thus, the solution to the equation is
\[
\boxed{-6}
\]