How do you solve and graph the inequality 4m-2<6 or 6m+2>2

Question

What does the "or" mean as well?

Answer 1

The word "or" implies two solutions while "and" would imply one.

Draw a number line. Mark zero in the middle, and indicate that the negative numbers on the left stretch to minus infinity; the positive numbers on the right extend to plus infinity.

4m-2<6; add 2 to both sides: 4m<8; divide through by 4: m<2. Mark 2 on the number line. The whole line to the left of that point is where m can be. 

6m+2>2; subtract 2 from each side: 6m>0, so m>0. In this solution the whole of the line to the right of zero is where m can be.

If "and" had been used instead of "or", m could only be in the segment between 0 and 2.