Math Snap

STEP 1

What is this asking?
We need to find the compound inequality that helps us solve for $x$ when the absolute value of $3x + 2$ is greater than $7$.
Watch out!
Remember, absolute value inequalities can be tricky!
Don't forget there are two conditions to consider when an absolute value is greater than a number.

STEP 2

1. Understand Absolute Value
2. Set up the Compound Inequality

STEP 3

Alright, let's break this down!
Absolute value, written as $| \text{something} |$, tells us how far that "something" is from zero.
Think of it like distance – it's always positive!

STEP 4

So, $|3x + 2| > 7$ means the "distance" of $3x + 2$ from zero is greater than 7.
This can happen in two ways: $3x + 2$ can be bigger than $7$ or smaller than $-7$.

STEP 5

If $3x + 2$ is bigger than $7$, we write it as $3x + 2 > 7$.

STEP 6

If $3x + 2$ is smaller than $-7$, we write it as $3x + 2 < -7$.

STEP 7

Since $3x + 2$ can be either greater than $7$ or less than $-7$, we join these inequalities with "or": $3x + 2 < -7$ or $3x + 2 > 7$.

The correct compound inequality is $3x + 2 < -7$ or $3x + 2 > 7$.