Question:
The solution set of the inequality $6(2x + 3) + x > 53 - 2x$ is
The solution set of the inequality $6(2x + 3) + x > 53 - 2x$ is
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When multiplying or dividing by a positive number, the inequality sign stays the same. Only flip the sign if you multiply/divide by a negative number.
Updated On: Jun 26, 2026
- $(\frac{7}{3}, \infty)$
- $(-\infty, \frac{7}{3})$
- $(\frac{7}{3}, 2)$
- $(-2, \frac{7}{3})$
- $(-\frac{7}{3}, \infty)$
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Solving a linear inequality involves isolating the variable $x$ on one side while maintaining the inequality relationship.
Step 2: Detailed Explanation:
1. Expand the terms in the inequality:
\[ 6(2x + 3) + x > 53 - 2x \]
\[ 12x + 18 + x > 53 - 2x \]
2. Combine like terms on the left side:
\[ 13x + 18 > 53 - 2x \]
3. Add $2x$ to both sides and subtract 18 from both sides:
\[ 13x + 2x > 53 - 18 \]
\[ 15x > 35 \]
4. Divide both sides by 15:
\[ x > \frac{35}{15} \]
5. Simplify the fraction by dividing by the common factor 5:
\[ x > \frac{7}{3} \]
In interval notation, $x > \frac{7}{3}$ is expressed as $(\frac{7}{3}, \infty)$.
Step 3: Final Answer:
The solution set is $(\frac{7}{3}, \infty)$.
Solving a linear inequality involves isolating the variable $x$ on one side while maintaining the inequality relationship.
Step 2: Detailed Explanation:
1. Expand the terms in the inequality:
\[ 6(2x + 3) + x > 53 - 2x \]
\[ 12x + 18 + x > 53 - 2x \]
2. Combine like terms on the left side:
\[ 13x + 18 > 53 - 2x \]
3. Add $2x$ to both sides and subtract 18 from both sides:
\[ 13x + 2x > 53 - 18 \]
\[ 15x > 35 \]
4. Divide both sides by 15:
\[ x > \frac{35}{15} \]
5. Simplify the fraction by dividing by the common factor 5:
\[ x > \frac{7}{3} \]
In interval notation, $x > \frac{7}{3}$ is expressed as $(\frac{7}{3}, \infty)$.
Step 3: Final Answer:
The solution set is $(\frac{7}{3}, \infty)$.
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