Questions: Solve the compound inequality. -3u < -18 and 4u - 5 > -29 Write the solution in interval notation. If there is no solution, enter ∅.

Solution Steps

To solve the compound inequality, we need to solve each inequality separately and then find the intersection of the solutions. For the first inequality, $-3u < -18$, we will isolate $u$ by dividing both sides by -3, remembering to reverse the inequality sign. For the second inequality, $4u - 5 > -29$, we will first add 5 to both sides and then divide by 4 to isolate $u$. Finally, we will find the intersection of the two solution sets and express it in interval notation.

The first inequality is:

$$-3u < -18$$

To solve for $u$, divide both sides by $-3$:

$$u > \frac{-18}{-3}$$

$$u > 6$$

The second inequality is:

$$4u - 5 > -29$$

First, add 5 to both sides:

$$4u > -29 + 5$$

$$4u > -24$$

Next, divide both sides by 4:

$$u > \frac{-24}{4}$$

$$u > -6$$

We have two inequalities:

1. $u > 6$
2. $u > -6$

The solution to the compound inequality is the intersection of these two solutions. Since $u > 6$ is more restrictive than $u > -6$, the solution is:

$$u > 6$$

Final Answer