Question

Solve the inequality and graph the solution on the line provided.
11, plus, 8, x, is greater than or equal to, minus, 45
11+8x≥
−45
Answer
Attempt 1 out of 2


Inequality Notation:
Number Line:

Answer 1

To solve the inequality \( 11 + 8x \geq -45 \), we will isolate \( x \).

1. **Subtract 11 from both sides:**
\[
11 + 8x - 11 \geq -45 - 11
\]
\[
8x \geq -56
\]

2. **Divide both sides by 8:**
\[
x \geq \frac{-56}{8}
\]
\[
x \geq -7
\]

### Inequality Notation:
The solution in inequality notation is:
\[
x \geq -7
\]

### Graph the Solution on a Number Line:
To graph the solution, draw a number line and mark the point -7. Since the inequality is \( \geq \), we will use a closed circle at -7 to indicate that -7 is included in the solution set. Shade all the numbers to the right of -7.

```
<---|----|----|----|----|----|----|----|----|--->
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
●========================>
```

In this graph:
- The closed circle at -7 represents that -7 is included in the solution set (because of the 'greater than or equal to' part).
- The shading to the right indicates all numbers greater than -7 are included in the solution.