Solve the inequality and graph the solution.

Question

20≤10(f–2)
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 \(20 \leq 10(f - 2)\), we can start by isolating \(f\).

1. Divide both sides of the inequality by \(10\): \[ 2 \leq f - 2 \]

2. Next, add \(2\) to both sides: \[ 2 + 2 \leq f \quad \Rightarrow \quad 4 \leq f \] This can be rewritten as: \[ f \geq 4 \]

Now that we have the solution, we can graph it.

Graphing the Solution

• The solution \(f \geq 4\) indicates that \(f\) can take any value greater than or equal to \(4\).
• On a number line, we will plot the point at \(4\).
  • Since \(f\) is greater than or equal to \(4\), we use a closed dot at \(4\) to indicate that \(4\) is included in the solution.
• We will shade to the right of this point to indicate all values greater than \(4\).

Instructions for the Graph

1. Plot the point at \(4\) with a closed dot (because \(f\) can equal \(4\)).
2. Shade to the right of \(4\) to represent all values greater than \(4\).

Based on your request to change an endpoint from closed to open:

• You could interpret that as removing the closed dot at \(4\) (although typically, for this inequality, it should be closed). If you want to change \(4\) to an open dot for illustrative purposes:
  • Change the dot at \(4\) to an open dot and keep shading to the right.

Final Notes

• The solution can now be summarized as \(f\) is in the interval \((4, \infty)\) if you choose to interpret \(4\) as open, or \([4, \infty)\) with \(4\) closed in a standard setting.