Question

What is the justification for each step in solving the inequality -7(3+8x) + 5x ≤ 1- 62x?
-7(3+8x) + 5x ≤ 1- 62x
-21 – 56x + 5x ≤ 1 – 62x
-21 – 51x ≤ 1 – 62x
-22 – 51x ≤ -62x
-22 ≤ -11x
2 ≥x

Answer 1

1. Given
2. Distributive Prop
3. Simplify
4. Sub Prop of Equality
5. Division Prop of Equality

Answer 2

-7(3+8x) + 5x ≤ 1- 62x solve parenthesis
-21 – 56x + 5x ≤ 1 – 62x solve parenthesis
-21 – 51x ≤ 1 – 62x combine like terms
-22 – 51x ≤ -62x solve integer
-22 ≤ -11x divide by integer
2 ≥x remember to flip inequality sign when you divide by a negative number

Answer 3

np

Answer 4

You should also try to memorize these properties, you'll use them all the time in pre-calc.

Answer 5

-7(3+8x) + 5x ≤ 1- 62x Given
-21 – 56x + 5x ≤ 1 – 62x Distributive property
-21 – 51x ≤ 1 – 62x Simplify
-22 – 51x ≤ -62x Subtraction property
-22 ≤ -11x Addition property
2 ≥x Division property