Question

Solve the inequality and graph the solution.
42≤26+8m

Answer 1

To solve the inequality \(42 \leq 26 + 8m\), we will isolate \(m\).

1. Subtract 26 from both sides:
\[
42 - 26 \leq 8m
\]
\[
16 \leq 8m
\]

2. Next, divide both sides by 8:
\[
\frac{16}{8} \leq m
\]
\[
2 \leq m
\]

This can be rewritten as:
\[
m \geq 2
\]

The solution to the inequality is \(m \geq 2\).

### Graphing the Solution

When graphing this inequality on a number line:

- Place an open circle (or a filled circle, depending on your notation) at 2 to indicate that \(m\) is included in the solution (since it is greater than or equal to).
- Shade the line to the right of 2 to represent all values of \(m\) that are greater than or equal to 2.

Here’s how the number line would look:

```
<---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8

●================>
```

The filled circle at 2 indicates that 2 is included in the solution, and the shaded area to the right indicates that all greater values are included.