Question

solve the inequality and graph the solution.
2 + 4u < 10
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 2 from both sides

$$2 + 4u-2<10 - 2$$
$$4u<8$$

Step2: Divide both sides by 4

$$\frac{4u}{4}<\frac{8}{4}$$
$$u < 2$$

To graph \(u < 2\) on the number - line:

• The endpoint is at \(u = 2\). Since the inequality is strict (\(<\)), we use an open circle at \(u = 2\).
• The solution set includes all real numbers less than 2, so we draw a ray to the left of \(u = 2\) on the number - line.

Answer:

The solution of the inequality \(2 + 4u<10\) is \(u < 2\). On the number - line, we have an open circle at \(2\) and a ray extending to the left.