Solve the inequality and graph the solution.

Question

10≥3(k+8)–8
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 \( 10 \geq 3(k + 8) - 8 \), we first simplify the expression on the right side.

1. Distribute the 3: \[ 10 \geq 3k + 24 - 8 \] This simplifies to: \[ 10 \geq 3k + 16 \]

2. Next, we isolate \( k \) by subtracting 16 from both sides: \[ 10 - 16 \geq 3k \] This simplifies to: \[ -6 \geq 3k \]

3. Now, divide both sides by 3 to solve for \( k \): \[ -2 \geq k \] or equivalently, \[ k \leq -2 \]

The solution to the inequality is \( k \leq -2 \).

Graphing the Solution:

1. Endpoints: The endpoint here is \( k = -2 \).

2. Choosing Closed or Open: Since the inequality is \( \leq \), we plot the endpoint at \( -2 \) as a closed point (solid dot).

3. Deleting Segment: Since \( k \) is less than or equal to \( -2 \), we draw a solid line extending to the left from the closed point at \( -2 \) to indicate all values less than \( -2 \).

Final Graph Representation:

• A solid dot at \( -2 \).
• A line extending to the left towards negative infinity.

In a graphical representation:

• A solid point at \( -2 \) represents that \( -2 \) is included in the solution.
• An arrow extending indefinitely to the left represents all values less than \( -2 \).

If you were to visualize it on a number line:

<----●========>
     -2

Where:

• \( -2 \) is closed (included).
• The line extends indefinitely to the left.