Multiply each term by the lowest common denominator, then solve the resulting equation. \( \begin{array}{ll}\text { a } \frac{x}{3}+\frac{x}{2}=5 & \text { b } \frac{a}{10}+\frac{a}{5}=3 \\ \text { d } \frac{k}{k}-\frac{t}{6}+\frac{t}{10}=8\end{array} \)

We'll solve each equation by first determining the lowest common denominator (LCD) for all terms, multiplying every term by that LCD, and then solving the resulting equation. ────────────────────────────── Problem (a): x/3 + x/2 = 5 1. The denominators are 3 and 2. The LCD is 6. 2. Multiply every term by 6:   6·(x/3) + 6·(x/2) = 6·5   2x + 3x = 30 3. Combine like terms:   5x = 30 4. Divide by 5:   x = 6 ────────────────────────────── Problem (b): a/10 + a/5 = 3 1. The denominators are 10 and 5. The LCD is 10. 2. Multiply every term by 10:   10·(a/10) + 10·(a/5) = 10·3   a + 2a = 30 3. Combine like terms:   3a = 30 4. Divide by 3:   a = 10 ────────────────────────────── Problem (d): k/k − t/6 + t/10 = 8 Note: Here k/k equals 1 (provided k ≠ 0). 1. The denominators are implicit 1 (from 1), 6, and 10. The LCD for 6 and 10 is 30 (since 1 is already covered by 30). 2. Multiply every term by 30:   30·(1) − 30·(t/6) + 30·(t/10) = 30·8   30 − 5t + 3t = 240 3. Combine like terms:   30 − 2t = 240 4. Subtract 30 from both sides:   −2t = 210 5. Divide by −2:   t = −105 ────────────────────────────── Final Answers: a. x = 6 b. a = 10 d. t = −105