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.

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
`(a)/(c)>(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\\\\(2x)/(2)>(10)/(2)\\\\x>5`