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# how do you write an absolute value inequality's solution in solution set?

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for ex:

$$|2x+2|≥ 2$$

$$|2x+1|<2$$

How do you write these in solution set form?? I am really confused and have an exam coming up!

All help is appreciated!!
thank you!

Sep 3, 2019

#1
+6046
+3

$$|2x+2|\geq 2\\~\\ 2x+2\geq 2 \Rightarrow x\geq 1\\ 2x+2 \leq -2 \Rightarrow x \leq -2\\~\\ S = \{x : x \in (-\infty, -2] \cup [1,\infty)\}$$

I leave the second one to you.

Sep 3, 2019

#1
+6046
+3

$$|2x+2|\geq 2\\~\\ 2x+2\geq 2 \Rightarrow x\geq 1\\ 2x+2 \leq -2 \Rightarrow x \leq -2\\~\\ S = \{x : x \in (-\infty, -2] \cup [1,\infty)\}$$

I leave the second one to you.

Rom Sep 3, 2019
#2
+681
0

thank you for your help!! i know how to solve them but like idk how to write them in solution set, like do we write it like this for the second one?
{x: -3/2 

Nirvana  Sep 3, 2019
edited by Nirvana  Sep 3, 2019
edited by Nirvana  Sep 3, 2019