Question
Which value of x satisfies the equation \( \frac{2}{3}\left(x+\frac{3}{2}\right)=\frac{1}{3} \) ?
Ask by Rowe Wade. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -1 \)
Solution
Solve the equation \( \frac{2}{3}\left(x+\frac{3}{2}\right)=\frac{1}{3} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{2}{3}\left(x+\frac{3}{2}\right)=\frac{1}{3}\)
- step1: Multiply the terms:
\(\frac{2}{3}x+1=\frac{1}{3}\)
- step2: Move the constant to the right side:
\(\frac{2}{3}x=\frac{1}{3}-1\)
- step3: Subtract the numbers:
\(\frac{2}{3}x=-\frac{2}{3}\)
- step4: Multiply by the reciprocal:
\(\frac{2}{3}x\times \frac{3}{2}=-\frac{2}{3}\times \frac{3}{2}\)
- step5: Multiply:
\(x=-1\)
The value of \( x \) that satisfies the equation \( \frac{2}{3}\left(x+\frac{3}{2}\right)=\frac{1}{3} \) is \( x = -1 \).
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Simplify this solution Extra Insights
To solve the equation \( \frac{2}{3}\left(x+\frac{3}{2}\right)=\frac{1}{3} \), we first eliminate the fraction by multiplying both sides by 3. This gives us: \[ 2\left(x+\frac{3}{2}\right) = 1 \] Next, divide both sides by 2: \[ x + \frac{3}{2} = \frac{1}{2} \] Now, subtract \( \frac{3}{2} \) from both sides: \[ x = \frac{1}{2} - \frac{3}{2} \] This simplifies to: \[ x = \frac{1 - 3}{2} = \frac{-2}{2} = -1 \] Therefore, the value of \( x \) that satisfies the equation is \( \boxed{-1} \).
