Question

Victor solved this inequality as shown: Step 1: 3x − 5 > x + 5 Step 2: 2x − 5 > 5 Step 3: 2x > 10 Step 4: x > 5 What property justifies the work between step 3 and step 4?

Answer 1

Answer: Division property of Inequality.

Step-by-step explanation:

For this case we know that:

- According to the Addition property of Inequality:

If $a>b$, then $a+c>b+c$

- Based on the Subtraction property of  Inequality:

If $a>b$, then $a-c>b-c$

- Based on the Multiplication property of  Inequality:

If $a>b$, then $a*c>b*c$  (If $c>0$)

- According to the Division property of  Inequality:

If $a>b$, then $\frac{a}{c}>\frac{b}{c}$ (If $c>0$)

Knowing these properties, we can identify  the property that justifies the work between Step 3 and Step 4. This is:

"Division property of Inequality"

Because he divided both sides of the inequality by 2:

$2x > 10\\\\\frac{2x}{2}>\frac{10}{2}\\\\x>5$