Solve the inequality and graph the solution.

Question

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20≥10(t+1)
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 \(-20 \geq 10(t + 1)\), we can begin by isolating \(t\).

1. Distribute the 10:

   \[ -20 \geq 10t + 10 \]

2. Subtract 10 from both sides:

   \[ -20 - 10 \geq 10t \] \[ -30 \geq 10t \]

3. Divide both sides by 10 (remember that dividing by a positive number does not change the direction of the inequality):

   \[ -3 \geq t \]

This can be rewritten as:

\[ t \leq -3 \]

Now, we can graph the solution \(t \leq -3\).

Graphing:

1. Endpoints: The endpoint is \(-3\).
2. Open or Closed: Since the inequality is less than or equal to (≤), we use a closed dot at \(-3\).
3. Direction: Since \(t\) can take any value less than or equal to \(-3\), we shade to the left (toward negative infinity).

Representation:

• The position of \(-3\) is marked with a closed dot, indicating that it is included in the solution set.
• The shaded line extending to the left indicates all values less than \(-3\).

Final Representation:

• The graph would show a closed dot at \(-3\) and a line extending to the left, indicating all values of \(t\) that satisfy the inequality.

If you have any further requests or need a visual reference, please let me know!

Answer 2

which way would it be shaded