Question
Solve the inequality for \( x \). \[ -7(x+5)+34>5(3-x) \] Simplify your answer as much as possible.
Ask by Whittaker Chandler. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x < -8 \)
Solution
1. Distribute the terms on both sides:
\[
-7(x+5) + 34 = -7x - 35 + 34 = -7x - 1
\]
\[
5(3-x) = 15 - 5x
\]
2. Write the inequality:
\[
-7x - 1 > 15 - 5x
\]
3. Add \(7x\) to both sides to gather \(x\) terms on the right:
\[
-1 > 15 + 2x
\]
4. Subtract \(15\) from both sides to isolate the term with \(x\):
\[
-16 > 2x
\]
5. Divide both sides by \(2\) (since \(2 > 0\), the inequality sign remains unchanged):
\[
-8 > x
\]
6. Write the final answer:
\[
x < -8
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
First, let's simplify the inequality step by step. Starting with the given inequality: \[ -7(x+5) + 34 > 5(3-x) \] Distribute on both sides: \[ -7x - 35 + 34 > 15 - 5x \] Now, combine the constants on the left side: \[ -7x - 1 > 15 - 5x \] Next, let's move the \( -5x \) term from the right side to the left side by adding \( 5x \) to both sides: \[ -7x + 5x - 1 > 15 \] \[ -2x - 1 > 15 \] Now, add 1 to both sides: \[ -2x > 16 \] Now, divide each side by -2. Remember that when you divide or multiply by a negative number, you must flip the inequality sign: \[ x < -8 \] So, the solution to the inequality is: \[ x < -8 \]
