To solve the inequality \(-20 \geq 10(t + 1)\), we can begin by isolating \(t\).
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Distribute the 10:
\[ -20 \geq 10t + 10 \]
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Subtract 10 from both sides:
\[ -20 - 10 \geq 10t \] \[ -30 \geq 10t \]
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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:
- Endpoints: The endpoint is \(-3\).
- Open or Closed: Since the inequality is less than or equal to (≤), we use a closed dot at \(-3\).
- 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!