Solve the inequality and graph the solution.

Question

1≤
u+12
10
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 \( \frac{u + 12}{10} \geq 1 \), follow these steps:

1. Start by isolating \( u \): \[ \frac{u + 12}{10} \geq 1 \]

2. Multiply both sides by 10 (since 10 is positive, the direction of the inequality does not change): \[ u + 12 \geq 10 \]

3. 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

1. Plot the endpoints: The endpoint for this inequality is \( -2 \).
2. Closed or open: Since the inequality is \( \geq \), we will use a closed dot for \( -2 \).
3. 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.