What should you do to solve the inequality: [tex]-96 \ < \ x + 42[/tex]?

A. Subtract 42 from both sides and flip to put the variable on the left.
B. Add 96 to both sides and flip to put the variable on the left.
C. Multiply by 96 on both sides and flip to put the variable on the left.
D. Add 42 to both sides.
E. Divide by 42 on both sides and flip to put the variable on the left.
F. Subtract 96 from both sides and flip to put the variable on the left.

To solve the inequality [tex]\(-96 < x + 42\)[/tex], follow these steps:

1. Identify the First Step: You want to isolate [tex]\(x\)[/tex] on one side of the inequality. To do this, you need to get rid of the [tex]\(+42\)[/tex] that's added to [tex]\(x\)[/tex]. The best way to remove [tex]\(+42\)[/tex] is to subtract 42 from both sides of the inequality.

2. Subtract 42 from Both Sides:
[tex]\[
-96 - 42 < x + 42 - 42
\][/tex]
Simplifying the right side, the [tex]\(42\)[/tex] cancels out:
[tex]\[
-96 - 42 < x
\][/tex]

3. Calculate the Left Side:
[tex]\[
-96 - 42 = -138
\][/tex]

4. Express the Final Inequality: Now, with the simplified left side, you have:
[tex]\[
-138 < x
\][/tex]

5. Rewrite the Inequality Flipping the Sides: To have [tex]\(x\)[/tex] on the left side (common practice), rewrite the inequality:
[tex]\[
x > -138
\][/tex]

So, the solution to the inequality is [tex]\(x > -138\)[/tex]. This tells us that [tex]\(x\)[/tex] must be greater than [tex]\(-138\)[/tex].