Question

Which value of x satisfies the equation one quarter, left parenthesis, x, plus, one fifth, right parenthesis, equals, minus, start fraction, 7, divided by, 10, end fraction
4
1
​
(x+
5
1
​
)=−
10
7
​
?
Answer

Answer 1

To solve the equation \( \frac{1}{4}(x + \frac{1}{5}) = -\frac{7}{10} \), we will follow these steps:

1. Eliminate the fraction by multiplying both sides of the equation by 4:
\[
x + \frac{1}{5} = -\frac{7}{10} \times 4
\]

2. Calculate the right side:
\[
-\frac{7}{10} \times 4 = -\frac{28}{10} = -\frac{14}{5}
\]

Now the equation is:
\[
x + \frac{1}{5} = -\frac{14}{5}
\]

3. Next, subtract \( \frac{1}{5} \) from both sides:
\[
x = -\frac{14}{5} - \frac{1}{5}
\]

4. Combine the fractions on the right side:
\[
x = -\frac{14 + 1}{5} = -\frac{15}{5} = -3
\]

So, the value of \( x \) that satisfies the equation is:
\[
\boxed{-3}
\]