Question
Which value of x satisfies the equation start fraction, 2, divided by, 3, end fraction, left parenthesis, x, plus, one third, right parenthesis, equals, start fraction, 56, divided by, 9, end fraction 3 2 (x+ 3 1 )= 9 56 ?
Answers
GPT-4o mini
To solve the equation
\[
\frac{2}{3} \left( x + \frac{1}{3} \right) = \frac{56}{9},
\]
we first eliminate the fraction on the left side by multiplying both sides by 3:
\[
2 \left( x + \frac{1}{3} \right) = \frac{56}{3}.
\]
Next, we distribute the 2 on the left:
\[
2x + \frac{2}{3} = \frac{56}{3}.
\]
Next, we can move \(\frac{2}{3}\) to the right side:
\[
2x = \frac{56}{3} - \frac{2}{3} = \frac{56 - 2}{3} = \frac{54}{3}.
\]
Now, simplify \(\frac{54}{3}\):
\[
2x = 18.
\]
Next, divide both sides by 2:
\[
x = 9.
\]
Thus, the value of \( x \) that satisfies the equation is
\[
\boxed{9}.
\]
\[
\frac{2}{3} \left( x + \frac{1}{3} \right) = \frac{56}{9},
\]
we first eliminate the fraction on the left side by multiplying both sides by 3:
\[
2 \left( x + \frac{1}{3} \right) = \frac{56}{3}.
\]
Next, we distribute the 2 on the left:
\[
2x + \frac{2}{3} = \frac{56}{3}.
\]
Next, we can move \(\frac{2}{3}\) to the right side:
\[
2x = \frac{56}{3} - \frac{2}{3} = \frac{56 - 2}{3} = \frac{54}{3}.
\]
Now, simplify \(\frac{54}{3}\):
\[
2x = 18.
\]
Next, divide both sides by 2:
\[
x = 9.
\]
Thus, the value of \( x \) that satisfies the equation is
\[
\boxed{9}.
\]