|y|>3 [ ]----][6.) |-3y|<18 [ ][-----][10.)|x-1|<4 [-----][14.) |x+5/ 3| <2?

Question

solve each absolute-value inequality ? please help me out seriously

Answer 1

|y| > 3
y > 3 And y < -1*3
y > 3 And y < -3
range of y = (-infinity, -3) (3, +infinity)

6.)
|-3y| < 18
-3y < 18 And -3y > -1*18
y > 18/-3 And -3y > -18
y > -18/3 And y < -18/-3
y > -6 And y < 6
range of y = (-6, 6)

10.)
|x - 1| < 4
x - 1 < 4 And x - 1 > -1 * 4
x < 4 + 1 And x - 1 > - 4
x < 5 And x > - 4 + 1
x < 5 And x > -3
range of x = (-3, 5)

14.)
|x + 5/3| < 2
x + 5/3 < 2 And x + 5/3 > -1*2
x < 2 - 5/3 And x + 5/3 > -2
x < 6/3 - 5/3 And x > -2 - 5/3
x < 1/3 And x > -6/3 - 5/3
x < 1/3 And x > -11/3
range of x = (-11/3, 1/3)

I hope this helped

Kia

Answer 2

|y|>3 This can be rewritten as -3 >y > 3

|-3y|<18
-18<-3y<18
-6 <-y < 6
6>y>-6

|x-1|<4
-4 < x-1 < 4
-3
|x+5/ 3| <2
-2 < (x+5)/3 <2
-6 < x+5 <12
-11 < x <7

This is the easiest way to handle these problems.