what does it do ?

Question

if i have I x+3 I< 5 WHAT DOES THE ABSLOUT DO FOR THAT EQUATION . HOW DOES THE ABSLOUT WORK AND CAN U SOLVE THISE PROBLEM FOR ME THANKX

is the answer x is in between or is or like x<9 or x>7 , 7

Answer 1

Everytime you have a variable inside an absolute value and an inequality, you'll branch off into two other inequalities. In general, if |y| < a (for some positive value a), then the inequality translates to

-a < y < a

In your case, since |x + 3| < 5, then

-5 < x + 3 < 5

And if we subtract 3 from all parts of the inequality, we get

-8 < x < 2

or, x is in the interval (-8,2)

Meaning x lies strictly between -8 and 2.

As a side note, when you have absolute value with equations, i.e.

|x + 3| = 5

which becomes

x + 3 = 5 and x + 3 = -5
x = 2 , x = -8
Therefore, x = {2, -8}

Secondary side note: if the absolute value of x + 3 is GREATER than 5, then we get an OR instead of an AND. Note that earlier, when |x+3| < 5, then we get an AND;
(x + 3 < 5) AND (-5 < (x + 3))

In the case of a greater sign, i.e. |x + 3| > 5, then
x + 3 > 5 OR x + 3 < -5

Therefore

x > 2 OR x < -8

and our interval is

x in the interval (-infinity, -8) U (2, infinity)

BOTTOM LINE: If you have an absolute value with an inequality and it's LESS than, it's an AND, i.e. |y| < a means (-a < y) AND (y < a).

If you have an absolute value with an inequality and it's MORE than, it's an OR: |y| > a implies (y > a) OR (y < -a).

Answer 2

*You have two inequalities: x + 3 < 5 and x + 3 > -5

1. solve the first inequality:

x + 3 < 5

First: subtract 3 from both sides:

x + 3 - 3 < 5 - 3
x < 2

2. solve the second inequality:

x + 3 > -5
x + 3 - 3 > -5 - 3
x > -8

answers: x < 2 and x > -8

Answer 3

this means that both of the following apply:
x + 3 < 5, and
-x - 3 <5

solve by isolating x:
x < 2
-x < 8, which means x > -8

-8 < x < 2 (x is between -8 and 2)

Answer 4

it means that values for x+3<-5 do not satisfy the inequality.

x<2 & x>-8 so -8

Answer 5

!x+3!<5
so x+3<5 and x+3>-5
if x+3<5
adding -3
x<2
if x+3>-5
adding -3
x>-8
=>-8 so the solution is -8

Answer 6

x+3<5
x+3<-5

x<2
x>-8

-8