Question

1.Solve the inequality. Show your work.
|r + 3| ≥ 7

Answer 1

Okay, whenever you see something of the form
|a| ≥ b

Your task will be to solve two inequalities, the first, simply removes the absolute value ||
a ≥ b
and the other, will be to reverse the inequality, and multiply one side by -1
a ≤ -b

Answer 2

so a ≤ -b is the answer

Answer 3

No.
Following that logic...
You get two inequalities to solve.
(1) Simply remove the absolute value sign ||
r + 3 ≥ 7

Please solve this inequality, for r.

Answer 4

4

Answer 5

r ≥ 4
That's one of them.

Now, solve for the other inequality
The one which switches the inequality, and multiplies the right side by -1
r+3 ≤ -7

Answer 6

?

Answer 7

The same way you got 4, now solve this
r + 3 ≤ -7

Answer 8

r<=-10

Answer 9

Very good :)
So, what's the interval notation for
r ≥ 4
?

And what's the interval notation for
r ≤ -10
?

Answer 10

?

Answer 11

Interval notation, like for
r ≥ 4, it would be
\[\Large [4 , \infty)\]

Answer 12

{-10}

Answer 13

∣r+3∣≥7
∗r+3≥7
r≥4
∗-(r+3)≥7
-r-3≥7
-r≥10
r≤-10