Question

Solve the inequality and graph the solution. (on a line plot, not a graph)
–
4(b+7)–3≥1

Answer 1

To solve the inequality \(-4(b + 7) - 3 \geq 1\), we will first simplify and isolate \(b\).

1. Distribute the \(-4\):
\[
-4b - 28 - 3 \geq 1
\]

2. Combine like terms:
\[
-4b - 31 \geq 1
\]

3. Add \(31\) to both sides:
\[
-4b \geq 1 + 31
\]
\[
-4b \geq 32
\]

4. Divide by \(-4\), remembering that dividing by a negative number reverses the inequality:
\[
b \leq -8
\]

The solution to the inequality is:
\[
b \leq -8
\]

### Graphing the Solution on a Number Line:
To represent this solution on a line plot, you would draw a number line and:

- Shade the portion of the line to the left of -8, indicating all numbers less than or equal to -8.
- Use a closed circle (or filled dot) at -8 to indicate that -8 is included in the solution set.

Here's how it will look:

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

*The "●" represents the closed circle at -8 and the shaded area to the left indicates all numbers less than -8.*