Math  /  Algebra

QuestionWhich compound inequality can be used to solve the inequality 3x+2>7|3 x+2|>7 ? 7<3x+2>7-7<3 x+2>7 7>3x+2>7-7>3 x+2>7 3x+2>73 x+2>-7 or 3x+2>73 x+2>7 3x+2<73 x+2<-7 or 3x+2>73 x+2>7

Studdy Solution

STEP 1

What is this asking? We need to find the compound inequality that helps us solve for xx when the absolute value of 3x+23x + 2 is greater than 77. 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 something| \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|3x + 2| > 7 means the "distance" of 3x+23x + 2 from zero is greater than **7**.
This can happen in two ways: 3x+23x + 2 can be *bigger* than 77 or *smaller* than 7-7.

STEP 5

If 3x+23x + 2 is bigger than 77, we write it as 3x+2>73x + 2 > 7.

STEP 6

If 3x+23x + 2 is smaller than 7-7, we write it as 3x+2<73x + 2 < -7.

STEP 7

Since 3x+23x + 2 can be *either* greater than 77 *or* less than 7-7, we join these inequalities with "or": 3x+2<73x + 2 < -7 or 3x+2>73x + 2 > 7.

STEP 8

The correct compound inequality is 3x+2<73x + 2 < -7 or 3x+2>73x + 2 > 7.

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