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]
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]
