Question

draw a number line shows the solution to the inequality? – 4x+8≤20

Answer 1

To solve the inequality \(-4x + 8 \leq 20\), follow these steps:

1. **Subtract 8 from both sides:**
\[
-4x \leq 20 - 8
\]
\[
-4x \leq 12
\]

2. **Divide by -4:** Remember to reverse the inequality sign when dividing by a negative number.
\[
x \geq \frac{12}{-4}
\]
\[
x \geq -3
\]

Now that we have the solution, \(x \geq -3\), we can draw the number line:

- Mark the point \(-3\) on the number line.
- Since \(x\) is greater than or equal to \(-3\), include a closed circle at \(-3\) (indicating that \(-3\) is part of the solution).
- Shade to the right of \(-3\) to indicate all values greater than \(-3\) are included in the solution.

Here is a simplified representation of what this would look like on a number line:

```
<----|----|----|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2 3 4
●====================>
```

In this representation:
- The dot (●) at \(-3\) is closed, indicating that \(-3\) is included.
- The line extending to the right indicates that all numbers greater than \(-3\) are included in the solution to the inequality.