Solve the inequality and graph the solution.

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.