Question

Solve the absolute value inequality: |5x + 3| ≥ 13

x ≤ -3.2 and x ≥ 2

x ≥ -3.2 or x ≤ 2

x ≤ -3.2 or x ≥ 2

x -3.2 or x ≥ 3.2

Answer 1

\[|x|>a\], with a>0, is the same as
x>a or x<-a
so rewrite your question like this:
\[5x+3 \ge 13 or 5x+3 \le -13\] and solve for x in both parts of the disjunction

Answer 2

@d im looking for a complete example so i could do the rest on my own thnks

Answer 3

ok
5x+3>=13
5x>=10
x>=2

5x+3<=-13
5x<=-16
x<=-16/5

So, x <=-16/5 or x>=2

Answer 4

-16/5=-3.2

Answer 5

so the first one just to clarify? @d

Answer 6

no, both. the solution set is {x|x<=-3.2 or x>=2}

Answer 7

ah the third one!

Answer 8

to remove the absolute value signs, you write a disjunction like I did