Question
Solve the inequality for \( u \). \[ 5 u-36 \geq-3(5-4 u) \] Simplify your answer as much as possible.
Ask by Barker Gardner. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( u \leq -3 \)
Solution
To solve the inequality:
\[
5u - 36 \geq -3(5 - 4u)
\]
**Step 1: Distribute the \(-3\) on the right-hand side.**
\[
5u - 36 \geq -15 + 12u
\]
**Step 2: Move all terms involving \(u\) to the left and constants to the right.**
Subtract \(12u\) from both sides:
\[
5u - 12u - 36 \geq -15
\]
\[
-7u - 36 \geq -15
\]
Add \(36\) to both sides:
\[
-7u \geq 21
\]
**Step 3: Solve for \(u\).**
Divide both sides by \(-7\). Remember to reverse the inequality sign when dividing by a negative number:
\[
u \leq -3
\]
**Final Answer:**
\[
u \leq -3
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the inequality \( 5u - 36 \geq -3(5 - 4u) \), we start by distributing the -3 on the right side: \[ 5u - 36 \geq -15 + 12u \] Next, we can get all terms involving \( u \) on one side and constant terms on the other side. We can do this by subtracting \( 12u \) from both sides and adding 36 to both sides: \[ 5u - 12u \geq -15 + 36 \] This simplifies to: \[ -7u \geq 21 \] Now, to solve for \( u \), we divide both sides by -7, remembering to flip the inequality sign when dividing by a negative number: \[ u \leq -3 \] Thus, the solution to the inequality is: \[ u \leq -3 \]
