Q:

What is the reason for each step in the solution of the inequality? 28−3(x−2)<5x+10Division Property of OrderSubtraction Property of OrderAddition Property of OrderDistributive PropertyCombine Like TermsGiven1. 28−3(x−2)<5x+102. 28−3x+6<5x+103. 34−3x<5x+104. 34<8x+105. 24<8x6. 3

Accepted Solution

A:
Answer:1. 28 − 3(x − 2) < 5x + 10            Given2. 28 − (3)(x) + (-3)(-2) < 5x + 10       Distributive Property a(b + c) = ab+ ac28 − 3x + 6 < 5x + 103.  (28 + 6) - 3x < 5x + 10             Combine Like Terms34 − 3x < 5x + 104. 34 - 3x + 3x < 5x + 3x + 10             Addition Property of Order34 < 8x + 105. 34 - 10 < 8x + 10 - 10        Subtraction Property of Order24 < 8x6. 24/8 < 8x/8        Division Property of Order3 < x