To solve the inequality \( \frac{u + 12}{10} \geq 1 \), follow these steps:
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Start by isolating \( u \): \[ \frac{u + 12}{10} \geq 1 \]
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Multiply both sides by 10 (since 10 is positive, the direction of the inequality does not change): \[ u + 12 \geq 10 \]
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Subtract 12 from both sides: \[ u \geq 10 - 12 \] \[ u \geq -2 \]
Thus, the solution to the inequality is: \[ u \geq -2 \]
Graphing the Solution
- Plot the endpoints: The endpoint for this inequality is \( -2 \).
- Closed or open: Since the inequality is \( \geq \), we will use a closed dot for \( -2 \).
- Graph the solution: Shade the line to the right of \( -2 \) to indicate all values greater than or equal to \( -2 \).
The graph will look like this:
<---●====================>
-2
- The closed dot at \( -2 \) indicates that \( -2 \) is included in the solution.
- The shaded line to the right indicates all numbers greater than \( -2 \) are included in the solution.