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.
[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.
