Question

What is the justification for each step in solving the inequality?

−7 (3 + 8x) + 5x ≤ 1 − 62x

Select from the drop-down menus to correctly justify each step.

−7 (3 + 8x) + 5x ≤ 1 − 62x Given

−21 − 56x + 5 x ≤ 1 − 62x Combine like terms or Distributive Property or Multiplication Property of Order

−21 − 51x ≤ 1 − 62x Choose: Addition Property of Order or Combine like terms or Multiplication Property of Order

−21 + 11x ≤ 1 Choose: Addition Property of Order or Division Property of Order or Multiplication Property of Order

11x ≤ 22 Addition Property of Order

x ≤ 2 Division Property of Order




What is the justification for each step in the solution of the equation?

54+2x=5x−3(2+6x)

Select from the drop-down menus to correctly justify each step.

54 + 2x = 5x - 3(2 + 6x)
- Given (EXAMPLE)

54 + 2x = 5x - 6 - 18x
Choose : Addition Property of Equality or Distributive Property or Multiplication Property of Equality

54 + 2x = -13x - 6
-Combine like terms

54 = -15x - 6
Subtraction Property of Equality

60 = -15x
Choose: Addition Property of Equality or Division Property of Equality or Multiplication Property of Equality

-4 = x
Choose: Addition Property of Equality or Division Property of Equality or Subtraction Property of Equality

Answer 1

-7 (3 + 8x) + 5 < = 1 - 62x....given
-21 - 56x + 5x < = 1 - 62x ...distributive property
-21 - 51x < = 1 - 62x...combine like terms
-21 + 11x < = 1....addition property
11x < = 22...addition property
x < = 2....division property
=================
54 + 2x = 5x - 3(2 + 6x)...given
54 + 2x = 5x - 6 - 18x....distributive property
54 + 2x = - 13x - 6...combine like terms
54 = -15x - 6...subtraction property
60 = -15x ...addition property
-4 = x....division property

Answer 2

Explanation:

(1)

1) given

-7 (3 + 8x) + 5 ≤ 1 - 62x

2) by distributive property..

-21 - 56x + 5x ≤ 1 - 62x

3) combine like terms

-21 - 51x ≤ 1 - 62x

4) using addition property of order

-21 + 11x ≤ 1

5) using addition property of order

11x ≤ 22

5) using division property of order

x ≤ 2

(2)

1) given that

54 + 2x = 5x - 3(2 + 6x)

2)using distributive property

54 + 2x = 5x - 6 - 18x

3)by combining like terms

54 + 2x = - 13x - 6

4)using subtraction property of equality

54 = -15x - 6

5)using addition property of equality

60 = -15x

6)using division property of equality

-4 = x