1. **State the problem:** Solve the equation for $t$ given by $$10 - 3t = 3t + 2.$$ 2. **Write the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equation. We can do this by adding or subtracting terms on both sides and then dividing if necessary. 3. **Step-by-step solution:** Start with the equation: $$10 - 3t = 3t + 2$$ Add $3t$ to both sides to move all $t$ terms to the right: $$10 = 3t + 3t + 2$$ $$10 = 6t + 2$$ Subtract 2 from both sides to isolate the term with $t$: $$10 - 2 = 6t$$ $$8 = 6t$$ Divide both sides by 6 to solve for $t$: $$t = \frac{8}{6}$$ Simplify the fraction by dividing numerator and denominator by 2: $$t = \frac{\cancel{8}^{4}}{\cancel{6}^{3}}$$ 4. **Final answer:** $$t = \frac{4}{3}$$ This means the value of $t$ that satisfies the equation is $\frac{4}{3}$.