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What is the solution to this inequality?

[tex]\frac{x}{9} + 7 \geq 10[/tex]

A. [tex]x \geq 83[/tex]
B. [tex]x \leq 83[/tex]
C. [tex]x \leq 27[/tex]
D. [tex]x \geq 27[/tex]

Answer :

Sure! Let's solve the inequality step by step:

We start with the inequality:

[tex]\[
\frac{x}{9} + 7 \geq 10
\][/tex]

1. Subtract 7 from both sides: We want to isolate the term with [tex]\(x\)[/tex], so we'll first get rid of the 7 on the left side by subtracting 7 from both sides of the inequality:

[tex]\[
\frac{x}{9} + 7 - 7 \geq 10 - 7
\][/tex]

This simplifies to:

[tex]\[
\frac{x}{9} \geq 3
\][/tex]

2. Multiply both sides by 9: Now we need to solve for [tex]\(x\)[/tex]. Since [tex]\(\frac{x}{9}\)[/tex] means [tex]\(x\)[/tex] divided by 9, we can get rid of the fraction by multiplying both sides of the inequality by 9:

[tex]\[
9 \cdot \frac{x}{9} \geq 3 \cdot 9
\][/tex]

This simplifies to:

[tex]\[
x \geq 27
\][/tex]

So, the solution to the inequality is [tex]\(x \geq 27\)[/tex]. The correct answer is:

D. [tex]\(x \geq 27\)[/tex]

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