1. **State the problem:** Solve the equation $$4 = 3 + |3 - \frac{1}{3} \times 2|$$. 2. **Understand the absolute value:** The absolute value $|x|$ represents the distance of $x$ from zero on the number line, so it is always non-negative. 3. **Simplify inside the absolute value:** Calculate the product inside the absolute value: $$\frac{1}{3} \times 2 = \frac{2}{3}$$ 4. **Rewrite the expression inside the absolute value:** $$3 - \frac{2}{3} = \frac{9}{3} - \frac{2}{3} = \frac{7}{3}$$ 5. **Evaluate the absolute value:** $$|\frac{7}{3}| = \frac{7}{3}$$ since $\frac{7}{3}$ is positive. 6. **Substitute back into the equation:** $$4 = 3 + \frac{7}{3}$$ 7. **Simplify the right side:** $$3 = \frac{9}{3}$$ so $$3 + \frac{7}{3} = \frac{9}{3} + \frac{7}{3} = \frac{16}{3}$$ 8. **Check if the equation holds:** $$4 = \frac{12}{3}$$ but the right side is $$\frac{16}{3}$$. Since $$\frac{12}{3} \neq \frac{16}{3}$$, the equation is false. **Final answer:** The equation $$4 = 3 + |3 - \frac{1}{3} \times 2|$$ is not true; there is no solution that satisfies it.