Question

Which graph represents the solution to the compound inequality?

–6 < 3x – 12 ≤ 9

Answer 1

2 < x ≤ 7 See below for explanation

Explanation:

Lets start by picking the inequality and summing 12 in all the parts, as we know this will not change the inequality:

–6 +12 < 3x – 12 +12 ≤ 9 +12

6 < 3x ≤ 21

Now lets divide all sides by 3:

6/3 < 3x/3 ≤ 21/3

2 < x ≤ 7

So, the x values that fit the inequality are those greater then 2 but less or equal to 7. The graph need to represent all this values. As we have only restriction for x -not for y- our graph will depend on the abscissa axis.

Here I attach the graph. Notice that the line that passes trough 2 is dotted, as those values do not fit the inequality. Try picking any pair (x,y) in this zone to see it verifies.