ex1.2_15

Example

Find the solution set for the compound inequality. Write the solution set in interval notation and graph it on a number line.

4u-4 < 0 \quad \mbox{and} \quad 3u-1 \ge -7

Solution

This compound inequality is an "AND" inequality. The solution set will be the intersection of the solution sets for each individual inequality. So, let's solve each individual inequality.

4u-4 <0

4u<4

u < 1

$(-\infty,1)$ .

Now we solve the second inequality.

3u-1 \ge -7

3u \ge -6

u \ge -2

$[-2,\infty)$ .

The solution of the compound inequality is the intersection (overlap) of the two intervals:

(-\infty,1) \cap [-2,\infty).

If we think about how the intervals overlap, we can simplify the intersection:

(-\infty,1) \cap [-2,\infty) = [-2,1).

Our final answer is the interval

[-2,1)

and its graph is

Number line shading numbers between -2 and 1, but not including 1