Question

What is the reason for each step in the solution of the inequality?

−2(x+3)−4>4x+30

Select the reason for each step from the drop-down menus.


−2(x+3)−4>4x+30 Given
−2x−6−4>4x+30
−2x−10>4x+30
−6x−10>30 Subtraction Property of Order
−6x>40
x<−203 Division Property of Order

Answer 1

The second one is Distributive property.
The third one is Combine Like Terms.
The fourth unanswered one is Addition Property of Order.

Answer 2

The correct answers are:

Distributive property; subtraction; addition property of equality.

Explanation:

To get from the first step to the second step, the terms inside parentheses have been multiplied by -2.  The property that allows us to multiply through parentheses, or distribute through parentheses, is the distributive property.

To get from the second step to the third step, the -6 and 4 have been subtracted; this means the reason for this is subtraction.

To get from the fourth step to the fifth step, 10 has been added to each side.  The addition property of equality allows us to do this.