How can we solve the equation \( \frac{2}{3} x + 4 = 2x \)?

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Solving the Equation \( \frac{2}{3} x + 4 = 2x \)

To solve the equation \( \frac{2}{3} x + 4 = 2x \), we will follow a series of steps to isolate the variable \( x \).

Step 1: Eliminate the Fraction

To make calculations easier, we can eliminate the fraction by multiplying every term in the equation by 3, which is the denominator of the fraction:

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

This simplifies to:

        2x + 12 = 6x

Step 2: Rearranging the Equation

Next, we will rearrange the equation by moving all terms involving \( x \) to one side and the constant terms to the other side. We can subtract \( 2x \) from both sides:

        12 = 6x - 2x

This simplifies to:

        12 = 4x

Step 3: Isolating \( x \)

Now, we need to isolate \( x \) by dividing both sides of the equation by 4:

        x = \frac{12}{4}

Thus, we find that:

        x = 3

Conclusion

The solution to the equation \( \frac{2}{3} x + 4 = 2x \) is \( x = 3 \). You can check your work by substituting \( x \) back into the original equation to ensure both sides are equal.

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