Question
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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

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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:** \[ u = \frac{8}{5} \]

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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 \[ u = 1.6. \]

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