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."
