solve for r and graph the solution. |r + 240| + 8

Question

solve for r and graph the solution. |r + 240| + 8 < 28 click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Accepted Answer

# Explanation:
## Step1: Isolate the absolute value
Subtract $8$ from both sides of the inequality $|r + 240|+8<28$.
$$|r + 240|+8-8<28 - 8$$
$$|r + 240|<20$$

## Step2: Apply the absolute - value inequality rule
If $|u|<a$ ($a>0$), then $-a < u < a$. Here $u=r + 240$ and $a = 20$.
$$-20<r + 240<20$$

## Step3: Solve for $r$
Subtract $240$ from all parts of the compound inequality.
$$-20-240<r+240 - 240<20-240$$
$$-260<r<-220$$

# Answer:
The solution of the inequality is $-260 < r<-220$. On the number - line, we have an open circle at $r=-260$ and an open circle at $r = - 220$, and the line segment between them is shaded.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Isolate the absolute value

Step2: Apply the absolute - value inequality rule

Step3: Solve for \(r\)

Answer: