Questions: Solve the equation for the indicated variable. 2/3 = 1/3(x-4)

Solve the equation for the indicated variable. 2/3 = 1/3(x-4)
Transcript text: Solve the equation for the indicated variable. \[ \frac{2}{3}=\frac{1}{3}(x-4) \]
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Solution

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Solution Steps

To solve the equation \(\frac{2}{3} = \frac{1}{3}(x-4)\) for \(x\), we can follow these steps:

  1. Eliminate the fraction by multiplying both sides of the equation by 3.
  2. Simplify the equation to isolate the term containing \(x\).
  3. Solve for \(x\) by adding or subtracting terms as necessary.
Step 1: Eliminate the Fraction

Starting with the equation: \[ \frac{2}{3} = \frac{1}{3}(x - 4) \] we multiply both sides by 3 to eliminate the fractions: \[ 2 = x - 4 \]

Step 2: Isolate the Variable

Next, we isolate \(x\) by adding 4 to both sides: \[ 2 + 4 = x \] which simplifies to: \[ x = 6 \]

Final Answer

\(\boxed{x = 6}\)

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