Question

Please i need help please help me out!

Answer 1

Answer:

1. 13 or -13

2. -5 < y < -3

3. 6 or -6

4. 1/8 or -1/8

Step-by-step explanation:

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x|

 For the Negative case we'll use -(x) 

For the Positive case we'll use (x) 

Step  3  :

Solve the Negative Case

      -(x) = 13 

     Multiply

      -x = 13 

     Multiply both sides by (-1)

      x = -13 

     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (x) = 13 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

 x=-13

 x=13

But for the case of question (2) its a different pattern..

Since this is a "less than" absolute-value inequality, my first step is to clear the absolute value according to the "less than" pattern. Then I'll solve the linear inequality.

| y + 4 | < 1

–1 < y + 4 < 1

This is the pattern for "less than". Continuing, I'll subtract 3 from all three "sides" of the inequality:

–1 – 4 < y + 4 - 4 < 1 – 4

–5 < y < -3

$- 5 < y < - 3$

The solution to the original absolute-value inequality, | y + 4 | <  1 , is the interval:

$- 5 < y < - 3$