Question

Select the correct answer.

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?

A.

division property of inequality

B.

inverse property of multiplication

C.

subtraction property of inequality

D.

transitive property of inequality

Answer 1

A. Division property of inequality

Step-by-step explanation:,

If a, b and c are any real numbers,

By the division property of inequality,

a = b ⇒
`(a)/(c)=(b)/(c)`,

By the inverse property of multiplication,

`a((1)/(a)) = 1`

where, 1 is multiplication identity.

By the subtraction property of inequality,

a = b ⇒ a - c = b - c

By transitive property of inequality,

a = b and b = c ⇒ a = c,

Thus, it is clear that,

Division property of inequality is used in step 4.

Option A is correct.