Question

What is the reason for each step in the solution of the inequality? 28−3(x−2)<5x+10

Division Property of Order

Subtraction Property of Order

Addition Property of Order

Distributive Property

Combine Like Terms

Given

1.

28−3(x−2)<5x+10

2.

28−3x+6<5x+10

3.

34−3x<5x+10

4.

34<8x+10

5.

24<8x

6.

3

Answer 1

1. 28 − 3(x − 2) < 5x + 10 Given

2. 28 − (3)(x) + (-3)(-2) < 5x + 10 Distributive Property a(b + c) = ab+ ac

28 − 3x + 6 < 5x + 10

3. (28 + 6) - 3x < 5x + 10 Combine Like Terms

34 − 3x < 5x + 10

4. 34 - 3x + 3x < 5x + 3x + 10 Addition Property of Order

34 < 8x + 10

5. 34 - 10 < 8x + 10 - 10 Subtraction Property of Order

24 < 8x

6. 24/8 < 8x/8 Division Property of Order

3 < x