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
?
Answer
Multiple Choice Answers
minus, 9−9
minus, 8−8
88
99
3
2
(x+
3
1
)=
9
56
?
Answer
Multiple Choice Answers
minus, 9−9
minus, 8−8
88
99
Answers
GPT-4o mini
To solve the equation
\[
\frac{2}{3} \left( x + \frac{1}{3} \right) = \frac{56}{9},
\]
first, we can eliminate the fraction on the left side by multiplying both sides by 3:
\[
2 \left( x + \frac{1}{3} \right) = \frac{56}{3}.
\]
Now, distribute the 2 on the left side:
\[
2x + \frac{2}{3} = \frac{56}{3}.
\]
Next, we can isolate \(2x\) by subtracting \(\frac{2}{3}\) from both sides:
\[
2x = \frac{56}{3} - \frac{2}{3} = \frac{56 - 2}{3} = \frac{54}{3} = 18.
\]
Next, divide both sides by 2 to solve for \(x\):
\[
x = \frac{18}{2} = 9.
\]
Thus, the value of \(x\) that satisfies the original equation is
\[
\boxed{9}.
\]
\[
\frac{2}{3} \left( x + \frac{1}{3} \right) = \frac{56}{9},
\]
first, we can eliminate the fraction on the left side by multiplying both sides by 3:
\[
2 \left( x + \frac{1}{3} \right) = \frac{56}{3}.
\]
Now, distribute the 2 on the left side:
\[
2x + \frac{2}{3} = \frac{56}{3}.
\]
Next, we can isolate \(2x\) by subtracting \(\frac{2}{3}\) from both sides:
\[
2x = \frac{56}{3} - \frac{2}{3} = \frac{56 - 2}{3} = \frac{54}{3} = 18.
\]
Next, divide both sides by 2 to solve for \(x\):
\[
x = \frac{18}{2} = 9.
\]
Thus, the value of \(x\) that satisfies the original equation is
\[
\boxed{9}.
\]