Question

Justify each step of this inequality by stating the property that was used to get to each step.

Given: -5(k+3)<12-10r+3r Property used:
Step 1: -5(k+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

issolat variable

subtract constant

individualize variable

divide by coeficient

answer

Explanation:

Answer 2

See below.

Explanation:

We have the inequality:

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

Step 1: Combining Like Terms:

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

Step 2: Distribute Property (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<27/2=13.5`

And we're done!