Questions: Solve 2 / 3(9c-3)=22.

Solve 2 / 3(9c-3)=22.
Transcript text: Solve $2 / 3(9 c-3)=22$.
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Solution

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Solution Steps

To solve the equation \( \frac{2}{3}(9c - 3) = 22 \), we need to isolate the variable \( c \). Here are the high-level steps:

  1. Distribute the \(\frac{2}{3}\) across the terms inside the parentheses.
  2. Simplify the resulting equation.
  3. Solve for \( c \) by isolating it on one side of the equation.
Step 1: Distribute the Fraction

First, distribute the \(\frac{2}{3}\) across the terms inside the parentheses: \[ \frac{2}{3}(9c - 3) = 22 \] \[ \frac{2}{3} \cdot 9c - \frac{2}{3} \cdot 3 = 22 \] \[ 6c - 2 = 22 \]

Step 2: Isolate the Variable

Next, isolate the variable \(c\) by adding 2 to both sides of the equation: \[ 6c - 2 + 2 = 22 + 2 \] \[ 6c = 24 \]

Step 3: Solve for \(c\)

Finally, solve for \(c\) by dividing both sides by 6: \[ c = \frac{24}{6} \] \[ c = 4 \]

Final Answer

\(\boxed{c = 4}\)

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