Inequality and Interval Notation

Question

How can I solve the following inequality:

-2(m-3)<5(m+1)-12

and how do I give both the inequality and interval notation forms of the solution?

Answer 1

Answer 2

-2(m-3)<5(m+1)-12

expand

-2m+6 <5m+5-12

combine like terms

6-5+12 <5m+2m

13< 7m

divide by 7

13/7 < m

which means the same as

m > 13/7

in interval notation (13/7, infinity)

check the 13/7, plug it into the original inequality, but treat it as an equation to find the end point or boundary of the inequality

-2(m-3) = 5(m+1)-12

-2(13/7-21/7) =5(13/7+7/7) -12

-2(-8/7) = 5(20/7) -12

16/7 =100/7-84/7

16/7 =16/7