Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.3: Introduction To Geometric Proof
Problem 36E: The Division Property of Inequality requires that we reverse the inequality symbol when dividing by...
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![**Question: Which values of \( x \) make the inequality true?**
Given inequality:
\[ 2(x - 4) - 9x \leq -4x + 13 \]
Options:
1. \( \{ x : x \geq 1 \} \)
2. \( \{ x : x \geq -7 \} \)
3. \( \{ x : x \leq 1 \} \)
4. \( \{ x : x \leq -7 \} \)
---
To solve the inequality, follow these steps:
1. Distribute the 2 on the left side of the inequality:
\[
2(x - 4) - 9x \leq -4x + 13 \implies 2x - 8 - 9x \leq -4x + 13
\]
2. Combine like terms on the left side:
\[
-7x - 8 \leq -4x + 13
\]
3. Add \(4x\) to both sides to get all \(x\) terms on one side:
\[
-7x + 4x - 8 \leq 13 \implies -3x - 8 \leq 13
\]
4. Add 8 to both sides:
\[
-3x \leq 21
\]
5. Divide by -3 and reverse the inequality sign:
\[
x \geq -7
\]
Thus, the correct set of values for \( x \) that satisfies the inequality is
\[ \{ x : x \geq -7 \} \]
which corresponds to the second option.
---
**Answer:** \( \{ x : x \geq -7 \} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fa1b26-ae8a-4ab4-a6dc-e4d6059f0f40%2Fe384c578-ba86-4351-acae-3be2eb9ba3c2%2Fwf04voj_processed.png&w=3840&q=75)
Transcribed Image Text:**Question: Which values of \( x \) make the inequality true?**
Given inequality:
\[ 2(x - 4) - 9x \leq -4x + 13 \]
Options:
1. \( \{ x : x \geq 1 \} \)
2. \( \{ x : x \geq -7 \} \)
3. \( \{ x : x \leq 1 \} \)
4. \( \{ x : x \leq -7 \} \)
---
To solve the inequality, follow these steps:
1. Distribute the 2 on the left side of the inequality:
\[
2(x - 4) - 9x \leq -4x + 13 \implies 2x - 8 - 9x \leq -4x + 13
\]
2. Combine like terms on the left side:
\[
-7x - 8 \leq -4x + 13
\]
3. Add \(4x\) to both sides to get all \(x\) terms on one side:
\[
-7x + 4x - 8 \leq 13 \implies -3x - 8 \leq 13
\]
4. Add 8 to both sides:
\[
-3x \leq 21
\]
5. Divide by -3 and reverse the inequality sign:
\[
x \geq -7
\]
Thus, the correct set of values for \( x \) that satisfies the inequality is
\[ \{ x : x \geq -7 \} \]
which corresponds to the second option.
---
**Answer:** \( \{ x : x \geq -7 \} \)
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