Question

Justify each step of this inequality by stating the property that was used to get to each step. Given: -5(r+3)<12-10r+3r Property used: Step 1: -5(r+3)<12-7r Step 1: Step 2: -5r-15<12-7r Step 2: Step 3: 2r-15<12 Step 3: Step 4: 2r<27 Step 4: Step 5: r<13.5 Step 5:

Answer 1

Step 1: Combining Like Terms

Step 2: Distributive Property

Step 3: Addition Property of Equality

Step 4: Addition Property of Equality

Step 5: Division Property of Equality

Answer 2

See below.

Explanation:

We have:

Given:

`-5(r+3)<12-10r+3r`

Step 1: Combining Like Terms (on the right):

`-5(r+3)<12-7r`

Step 2: Distributive Property (distribute the -5 on the left):

`-5r-15<12-7r`

Step 3: Addition Property of Equality (add 7r to both sides):

`2r-15<12`

Step 4: Addition Property of Equality (add 15 to both sides):

`2r<27`

Step 5: Division Property of Equality (divide both sides by 2):

`r<13.5`

And we're done!