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Solve the following inequality for [tex]$x$[/tex].

[tex] x - 9 \leq 2(9 - x) [/tex]

A. [tex] x \leq 9 [/tex]

B. [tex] x \geq 11 [/tex]

C. [tex] x \ \textless \ -7 [/tex]

D. [tex] x \ \textless \ 10 [/tex]

Sagot :

GinnyAnswer
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]
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