Question

Which value of x satisfies the equation start fraction, 3, divided by, 4, end fraction, left parenthesis, x, plus, start fraction, 2, divided by, 5, end fraction, right parenthesis, equals, minus, start fraction, 9, divided by, 20, end fraction
4
3
​
(x+
5
2
​
)=−
20
9
​
?
Answer
Multiple Choice Answers
1
2
minus, 2
minus, 1

Answer 1

To solve the equation

\[
\frac{3}{4} \left( x + \frac{2}{5} \right) = -\frac{9}{20},
\]

let's start by eliminating the fraction on the left side. We can do this by multiplying both sides of the equation by \( 4 \):

\[
3 \left( x + \frac{2}{5} \right) = -\frac{9}{20} \times 4.
\]

Calculating the right side:

\[
-\frac{9 \times 4}{20} = -\frac{36}{20} = -\frac{9}{5}.
\]

Now the equation simplifies to:

\[
3 \left( x + \frac{2}{5} \right) = -\frac{9}{5}.
\]

Next, divide both sides by \( 3 \):

\[
x + \frac{2}{5} = -\frac{9}{15}.
\]

Now we simplify \(-\frac{9}{15}\):

\[
-\frac{9}{15} = -\frac{3}{5}.
\]

So now we have:

\[
x + \frac{2}{5} = -\frac{3}{5}.
\]

Next, subtract \(\frac{2}{5}\) from both sides:

\[
x = -\frac{3}{5} - \frac{2}{5}.
\]

Now combine the fractions:

\[
x = -\frac{3 + 2}{5} = -\frac{5}{5} = -1.
\]

Thus, the solution to the equation is

\[
\boxed{-1}.
\]