Solve the inequality and graph the solution.

Question

18≥6(u–5)
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 \( 18 \geq 6(u - 5) \):

1. Start by distributing on the right side: \[ 18 \geq 6u - 30 \]

2. Next, add 30 to both sides: \[ 48 \geq 6u \] or, equivalently: \[ 6u \leq 48 \]

3. Now, divide both sides by 6: \[ u \leq 8 \]

The solution to the inequality is: \[ u \leq 8 \]

Graphing the Solution

To graph the solution \( u \leq 8 \):

1. Identify the endpoints: The endpoint is \( u = 8 \).
2. Select the type of endpoint: Since the inequality is "less than or equal to" (\(\leq\)), we will use a closed circle at \( u = 8 \) to indicate that 8 is included in the solution.
3. Delete the other part of the line: This means you'll shade to the left of \( u = 8 \).

Final Graph

• A closed dot at \( u = 8 \).
• A shaded line extending to the left from this dot, indicating all values less than or equal to 8 are included.

In a number line representation, it looks like this:

<---●=======>
     8

Where:

• The circle at \( 8 \) is closed (included in the solution).
• The line extends to the left, indicating all numbers less than \( 8 \) are included.

Summary

The solution is: \[ u \leq 8 \] And the graphical representation shows a closed circle at 8, with the line extending to the left.