Solve the inequality and graph the solution.

Question

4(u–2)<16
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 4(u - 2) < 16 \), we start by distributing and isolating \( u \):

1. Distribute the 4: \[ 4u - 8 < 16 \]

2. Add 8 to both sides: \[ 4u < 16 + 8 \] \[ 4u < 24 \]

3. Divide by 4: \[ u < 6 \]

So the solution to the inequality is \( u < 6 \).

Graphing the solution:

• We will plot the endpoint at \( u = 6 \).
• Since \( u < 6 \) does not include 6 (it's an open interval), we will use an open circle at 6.
• The solution extends to the left of 6, so we will have a ray that continues to the left without an endpoint.

Graph:

• Endpoint at \( 6 \): open circle (since 6 is not included)
• Middle segment: everything to the left of 6, which is represented as: \[ \text{---} \text{(open circle at 6)} \text{---} \] (There are no changes needed in this part of the line, as we're simply highlighting all values less than 6.)

So overall, the graph would look like this:

---(6)------------------>

Here the parentheses indicate that 6 is not included in the solution.