Question

1. |x+3|=4

x = 1, -7

2. |x-2|=6
x = 8, -4

3. |x-5|<3
x = ??

4. |2x+3|>*17
x = ??

[>* means greater/less than OR equal to]

Please check.
And show how to do numbers 3 and 4.
Thank you.

Answer 1

first two are correct

#3
|x-5|<3
(x-5) < 3 AND -(x-5) < 3
x < 8 AND -x < -2
x < 8 AND x > 2

so 2 < x < 8

for #4
|2x+3| ≥ 17
2x+3 ≥ 17 OR -2x-3 ≥ 17
x ≥ 7 OR x ≤ -10