Question

Solve the compound inequality.

3u-3> 15
and
2u - 4>2
Write the solution in interval notation.
If there is no solution, enter Ø.

Answer 1

To solve the given compound inequality, we solve each inequality separately and then find their intersection. The final solution is u > 6, which is expressed in interval notation as (6, +infinity).

Step-by-step explanation:

To solve the compound inequality 3u-3 > 15 and 2u - 4 > 2, we tackle each inequality separately first. For the first inequality:

1. Add 3 to both sides: 3u > 18.
2. Divide both sides by 3: u > 6.

For the second inequality:

1. Add 4 to both sides: 2u > 6.
2. Divide both sides by 2: u > 3.

Since we are looking for u that satisfies both inequalities, we take the intersection of the two solutions. Since u > 6 covers u > 3 (anything greater than 6 is, of course, greater than 3), the solution to the compound inequality is simply u > 6.

The solution in interval notation is (6, +infinity).