Solve the algebraic equation to find the value of 3x - 2.

Let’s solve the equation step by step.

We are given:

> Equation:
> $\frac{2}{3}(9x - 6) - 4 = 9x - 6$

And we are asked to find the value of:
> $3x - 2$

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Step 1: Simplify the left side

Start with:
$\frac{2}{3}(9x - 6) - 4$

Distribute $\frac{2}{3}$ into $(9x - 6)$:

- $\frac{2}{3} \cdot 9x = \frac{18x}{3} = 6x$
- $\frac{2}{3} \cdot (-6) = \frac{-12}{3} = -4$

So, $\frac{2}{3}(9x - 6) = 6x - 4$

Now subtract 4 more (from the original expression):

Left side becomes:
$6x - 4 - 4 = 6x - 8$

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Step 2: Write the simplified equation

Original equation was:

$\frac{2}{3}(9x - 6) - 4 = 9x - 6$

After simplifying left side:

$6x - 8 = 9x - 6$

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Step 3: Solve for x

Subtract $6x$ from both sides:

$-8 = 3x - 6$

Add 6 to both sides:

$-2 = 3x$

Divide both sides by 3:

$x = -\frac{2}{3}$

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Step 4: Find the value of $3x - 2$

Plug in $x = -\frac{2}{3}$:

$3x - 2 = 3 \cdot \left(-\frac{2}{3}\right) - 2 = -2 - 2 = -4$

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✔ Final Answer: A) –4

Final Answer: A