High School

Which one of the choices below is the solution to the inequality [tex]x - 9 \geq 7[/tex]?

A. [tex]x \geq -2[/tex]
B. [tex]x \leq -2[/tex]
C. [tex]x \geq 16[/tex]
D. [tex]x \leq 16[/tex]

Answer :

To solve the inequality [tex]\(x - 9 \geq 7\)[/tex], we need to find the value of [tex]\(x\)[/tex] that makes this statement true.

1. Start with the inequality:
[tex]\[
x - 9 \geq 7
\][/tex]

2. Add 9 to both sides to isolate [tex]\(x\)[/tex]. This step will help us to get rid of the [tex]\(-9\)[/tex] on the left side:
[tex]\[
x - 9 + 9 \geq 7 + 9
\][/tex]

3. Simplify both sides:
[tex]\[
x \geq 16
\][/tex]

Thus, the solution to the inequality is [tex]\(x \geq 16\)[/tex]. This means that any value of [tex]\(x\)[/tex] that is 16 or greater satisfies the inequality.

Therefore, the correct choice from the given options is:
[tex]\(x \geq 16\)[/tex]

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