Answered

Kendall is solving this inequality:

[tex]\[ \frac{x}{2} + 6 \ \textgreater \ 42 \][/tex]

What should she do first to solve?

A. Add 42 to both sides of the inequality
B. Add 6 to both sides of the inequality
C. Divide both sides of the inequality by 2
D. Subtract 6 from both sides of the inequality



Answer :

To solve the inequality:

[tex]\[ \frac{x}{2} + 6 > 42 \][/tex]

The goal is to isolate the variable [tex]\( x \)[/tex]. Here’s a detailed step-by-step solution:

1. Identify the inequality:
[tex]\[ \frac{x}{2} + 6 > 42 \][/tex]

2. Move the constant term: We need to isolate the term containing [tex]\( x \)[/tex]. To do this, we should first remove the constant term on the left side of the inequality.

The constant term here is [tex]\( +6 \)[/tex]. To eliminate this, we subtract 6 from both sides of the inequality. This step simplifies the expression.

3. Apply the operation:
[tex]\[ \frac{x}{2} + 6 - 6 > 42 - 6 \][/tex]

4. Simplify the inequality:
[tex]\[ \frac{x}{2} > 36 \][/tex]

By subtracting 6 from both sides of the inequality, we've successfully simplified it to [tex]\(\frac{x}{2} > 36\)[/tex].

So, the first step Kendall should take to solve this inequality is:
[tex]\[ \boxed{\text{Subtract 6 from both sides of the inequality}} \][/tex]