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

Answer :

We begin with the inequality
[tex]$$
\frac{x}{9} + 7 \geq 10.
$$[/tex]

Step 1: Subtract 7 from both sides

Subtracting 7 from both sides of the inequality gives:
[tex]$$
\frac{x}{9} + 7 - 7 \geq 10 - 7,
$$[/tex]
which simplifies to:
[tex]$$
\frac{x}{9} \geq 3.
$$[/tex]

Step 2: Multiply both sides by 9

Since [tex]$9$[/tex] is a positive number, multiplying both sides by [tex]$9$[/tex] does not change the direction of the inequality. Thus, we have:
[tex]$$
9 \cdot \frac{x}{9} \geq 3 \cdot 9.
$$[/tex]
This simplifies to:
[tex]$$
x \geq 27.
$$[/tex]

Therefore, the solution to the inequality is:
[tex]$$
x \geq 27.
$$[/tex]

This corresponds to option B.

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