Question

solve the inequality and graph the solution.
-m + 6 < 8
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
the segment, ray, or line to delete it.

Explanation:

Step1: Subtract 6 from both sides

$$\begin{align*} -m+6 - 6&<8 - 6\\ -m&<2 \end{align*}$$

Step2: Multiply both sides by -1 and reverse the inequality sign

When we multiply or divide an inequality by a negative number, the direction of the inequality sign changes.

$$\begin{align*} (-1)\times(-m)&>(-1)\times2\\ m&>- 2 \end{align*}$$

To graph the solution \(m > - 2\):

• The endpoint is at \(m=-2\). Since the inequality is \(>\) (not \(\geq\)), we use an open circle at \(m =-2\).
• Then we draw a ray to the right of \(m=-2\) (because \(m\) is greater than \(-2\))

Answer:

The solution of the inequality is \(m > - 2\). On the number - line, we have an open circle at \(-2\) and a ray extending to the right.