Question
Solve for \( u \). \[ 29=3(u+7)+2 u \] Simplify your answer as much as possible.
Ask by Tucker Ellis. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( u = \frac{8}{5} \)
Solution
To solve the equation for \( u \):
\[
29 = 3(u + 7) + 2u
\]
**Step 1: Expand the Equation**
First, distribute the 3 into the parentheses:
\[
29 = 3u + 21 + 2u
\]
**Step 2: Combine Like Terms**
Combine the terms involving \( u \):
\[
29 = (3u + 2u) + 21 \\
29 = 5u + 21
\]
**Step 3: Isolate \( u \)**
Subtract 21 from both sides to get the terms with \( u \) by themselves:
\[
29 - 21 = 5u \\
8 = 5u
\]
**Step 4: Solve for \( u \)**
Divide both sides by 5:
\[
u = \frac{8}{5}
\]
**Final Answer:**
\[
u = \frac{8}{5}
\]
Reviewed and approved by the UpStudy tutoring team
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Bonus Knowledge
To solve for \( u \) in the equation \[ 29 = 3(u + 7) + 2u, \] we start by distributing the \( 3 \) on the right side: \[ 29 = 3u + 21 + 2u. \] Next, we combine like terms: \[ 29 = 5u + 21. \] Now, we isolate \( 5u \) by subtracting \( 21 \) from both sides: \[ 29 - 21 = 5u, \] \[ 8 = 5u. \] Finally, we solve for \( u \) by dividing both sides by \( 5 \): \[ u = \frac{8}{5}. \] So the solution is \[ u = 1.6. \]