Let's solve the inequality step by step and identify the properties used in each step.
### Given
[tex]\[ 3x - 2 > -4 \][/tex]
### Step 1
Justification:
This is the initial inequality we are given to solve.
### Step 2
Add 2 to both sides:
This step involves using the Addition Property of Inequality. The Addition Property of Inequality states that if you add the same number to both sides of an inequality, the inequality remains true.
[tex]\[ 3x - 2 + 2 > -4 + 2 \][/tex]
[tex]\[ 3x > -2 \][/tex]
### Step 3
Divide both sides by 3:
This step involves using the Division Property of Inequality. The Division Property of Inequality states that if you divide both sides of an inequality by a positive number, the inequality remains true. (Note: The direction of the inequality would reverse if we were dividing by a negative number, but in this case, we are dividing by the positive number 3.)
[tex]\[ \frac{3x}{3} > \frac{-2}{3} \][/tex]
[tex]\[ x > -\frac{2}{3} \][/tex]
### Summary
- Step 1: Given the original inequality [tex]\( 3x - 2 > -4 \)[/tex].
- Step 2: Adding 2 to both sides (Addition Property of Inequality) to get [tex]\( 3x > -2 \)[/tex].
- Step 3: Dividing both sides by 3 (Division Property of Inequality) to get [tex]\( x > -\frac{2}{3} \)[/tex].
