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Identify the property used in each step of solving the inequality [tex]\( 3x - 2 \ \textgreater \ -4 \)[/tex].

| Step | Justification |
|--------------|-----------------------------------|
| [tex]\( 3x - 2 \ \textgreater \ -4 \)[/tex] | Given |
| [tex]\( 3x \ \textgreater \ -2 \)[/tex] | Addition Property of Inequality |
| [tex]\( x \ \textgreater \ -\frac{2}{3} \)[/tex] | Division Property of Inequality |



Answer :

GinnyAnswer
Sure, let's go through the steps and identify the properties used in each justification.

### Steps and Justifications

1. Step 1: Given

The inequality given is [tex]\( 3x - 2 > -4 \)[/tex].

Justification 1: Given

2. Step 2: Add 2 to both sides

To isolate the term involving [tex]\( x \)[/tex], we add 2 to both sides of the inequality:
[tex]\[ 3x - 2 + 2 > -4 + 2 \][/tex]
This simplifies to:
[tex]\[ 3x > -2 \][/tex]

Justification 2: Add 2 to both sides

3. Step 3: Divide both sides by 3

Finally, to solve for [tex]\( x \)[/tex], we divide both sides of the inequality by 3:
[tex]\[ \frac{3x}{3} > \frac{-2}{3} \][/tex]
This simplifies to:
[tex]\[ x > -\frac{2}{3} \][/tex]

Justification 3: Divide both sides by 3

### Summary

In summary, the detailed step-by-step solution for solving the inequality [tex]\( 3x - 2 > -4 \)[/tex] and identifying the justification for each step is as follows:

1. Given:
[tex]\[ 3x - 2 > -4 \][/tex]

2. Add 2 to both sides:
[tex]\[ 3x > -2 \][/tex]

3. Divide both sides by 3:
[tex]\[ x > -\frac{2}{3} \][/tex]

The justifications for each step are correctly identified respectively as "Given," "Add 2 to both sides," and "Divide both sides by 3."

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