Question

Is this right or wrong?
11. Solve the inequality. Show your work.
|r + 3| ≥ 7

| r + 3|≥ 7
-3 -3
| r | ≥ 4
If I plug the the 4 into r's place
|4+3| ≥7

Answer 1

for absolute value problem, you need do:
\(| r+3|\geq 7\)
\(-7\geq r+3\geq 7\)
\(\bullet \) first and middle : \(-7 \geq r+3 \)
-3 both sides \(-11\geq r\), that means \(r\leq -11\) (namely *)
\(\bullet\) middle and last: \(r+3\geq 7\)
-3 both sides, \(r\geq 4\) (namely **)

Combine * and **, you have either \(r\leq -11\) or \(r\geq 4\) is the solution for the expression.

Answer 2

Hence, your answer should be both with OR between them. I meant \(r\leq -11\) OR \(r\geq 4\)

Answer 3

So i have to move my 7 over to the left?

Answer 4

Okay.

Answer 5

Actually, you NOT move 7, just put -7 to the left.

Answer 6

Do the original 7 stay on or do i subtract it?

Answer 7

stay!! just put an extra value by opposite of 7 to the left.

Answer 8

In general, if |a| < 7, to solve it, you put one more value on the left by opposite value of number , like -7<a<7

Answer 9

Okay. Do i include it when i'm subtarcting 3?

Answer 10

if |a|> 7, again, put one more value on the left
-7 >a >7
On that way, you take off the absolute sign and solve part by part like above.

Answer 11

After taking off the absolute value sign, you solve as usual, no absolute value any more.

Answer 12

Alright. So i won't need the bars anymore?

Answer 13

yup