Answer :
Let's solve the inequality step-by-step:
Given inequality:
[tex]\[ x - 9 \leq 2(9 - x) \][/tex]
1. Distribute the 2 on the right side of the inequality:
[tex]\[ x - 9 \leq 2 \cdot 9 - 2 \cdot x \][/tex]
[tex]\[ x - 9 \leq 18 - 2x \][/tex]
2. Combine like terms by adding [tex]\(2x\)[/tex] to both sides:
[tex]\[ x + 2x - 9 \leq 18 \][/tex]
[tex]\[ 3x - 9 \leq 18 \][/tex]
3. Isolate the term [tex]\(3x\)[/tex] by adding 9 to both sides:
[tex]\[ 3x - 9 + 9 \leq 18 + 9 \][/tex]
[tex]\[ 3x \leq 27 \][/tex]
4. Divide both sides of the inequality by 3:
[tex]\[ x \leq \frac{27}{3} \][/tex]
[tex]\[ x \leq 9 \][/tex]
Therefore, the correct answer is:
[tex]\[ A. \ x \leq 9 \][/tex]
Given inequality:
[tex]\[ x - 9 \leq 2(9 - x) \][/tex]
1. Distribute the 2 on the right side of the inequality:
[tex]\[ x - 9 \leq 2 \cdot 9 - 2 \cdot x \][/tex]
[tex]\[ x - 9 \leq 18 - 2x \][/tex]
2. Combine like terms by adding [tex]\(2x\)[/tex] to both sides:
[tex]\[ x + 2x - 9 \leq 18 \][/tex]
[tex]\[ 3x - 9 \leq 18 \][/tex]
3. Isolate the term [tex]\(3x\)[/tex] by adding 9 to both sides:
[tex]\[ 3x - 9 + 9 \leq 18 + 9 \][/tex]
[tex]\[ 3x \leq 27 \][/tex]
4. Divide both sides of the inequality by 3:
[tex]\[ x \leq \frac{27}{3} \][/tex]
[tex]\[ x \leq 9 \][/tex]
Therefore, the correct answer is:
[tex]\[ A. \ x \leq 9 \][/tex]
