Question

Graph the solution to this inequality on the number line.
2x – 6 > -16 and 3x – 10 < 8

Answer 1

2x-6=-16 and 3x- 10=8

Explanation:

2x=-16+6 and 3x=8+10

2x=-10 and 3x=18

2x/2=10/2 and 3x/3=18/3

x=5 and X=6

Answer 2

The intersection of the solution set consists of the elements that are contained in all the intervals. -5 < x < 6.

Solving compound inequalities.

A compound inequality is the combination of two or more inequalities and they are associated by the word (and) or (or). In the given compound inequality, we have:

2x - 6 > - 16 and 3x - 10 < 8

Start with the first part of the inequality we have;
2x - 6 > - 16

2x > - 16 + 6

2x > - 10

x > -5

Also, 3x -10 < 8

3x < 8 + 10

3x < 18

x < 6

Therefore, the intersection of the solution set consists of the elements that are contained in all the intervals. -5 < x < 6.