Question
8. \( \frac{1}{3}(t+4)=2+\frac{3t}{2} \)
Ask by Owen Powell. in Indonesia
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( t = -\frac{4}{7} \)
Solution
To solve the equation:
\[
\frac{1}{3}(t + 4) = 2 + \frac{3t}{2}
\]
**Step 1: Eliminate the Fractions**
Multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 6:
\[
6 \times \frac{1}{3}(t + 4) = 6 \times \left(2 + \frac{3t}{2}\right)
\]
**Step 2: Simplify Each Term**
\[
2(t + 4) = 12 + 9t
\]
**Step 3: Distribute on the Left Side**
\[
2t + 8 = 12 + 9t
\]
**Step 4: Get All \( t \)-Terms on One Side and Constants on the Other**
Subtract \( 2t \) from both sides:
\[
8 = 12 + 7t
\]
Subtract 12 from both sides:
\[
-4 = 7t
\]
**Step 5: Solve for \( t \)**
\[
t = \frac{-4}{7}
\]
\[
t = -\frac{4}{7}
\]
**Answer:** \( t = -\dfrac{4}{7} \)
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Simplify this solution Bonus Knowledge
To solve the equation \( \frac{1}{3}(t+4)=2+\frac{3t}{2} \), start by eliminating the fraction on the left. Multiply both sides by 3 to get \( t+4 = 6 + \frac{9t}{2} \). Next, to eliminate the fraction on the right, multiply the entire equation by 2, leading to \( 2(t+4) = 2(6) + 9t \). Simplifying further gives \( 2t + 8 = 12 + 9t \). Now, move all terms involving \( t \) to one side and the constant terms to the other: \( 2t - 9t = 12 - 8 \), resulting in \( -7t = 4 \). Finally, divide by -7 to find \( t = -\frac{4}{7} \). So, the solution to the equation is \( t = -\frac{4}{7} \).
