SOLUTION: Solve the following inequality: |x+1|>= x-3. (The absolute value of X+1 is greater than or equal to x-3). Please show your work.

Algebra ->  Graphs -> SOLUTION: Solve the following inequality: |x+1|>= x-3. (The absolute value of X+1 is greater than or equal to x-3). Please show your work.      Log On


   

Question 905757: Solve the following inequality: |x+1|>= x-3. (The absolute value of X+1 is greater than or equal to x-3). Please show your work.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for two situations.

x+1 is zero or positive gives x%2B1%3E=x-3
and therefore all x values for x%3E=-1 will work.

x+1 negative or less than zero gives -x-1%3E=x-3
-2x-1%3E=-3
2x%2B1%3C=3
2x%3C=2
x%3C=1

Just to be sure, use -1 and 1 as critical values making the number line into three intervals, and check in each interval for truth or falsity.

x%3C=-1
try x at -4.
abs(-4+1)>=-4-3
abs(-3)>=-7
3>=-7
TRUE. x%3C=-1 works.

-1%3C=x%3C=1
Try x at 0.
abs%280%2B1%29%3E=0-3
1%3E=-3
TRUE. -1%3C=x%3C=1 works.

1%3C=x
try x at 5.
abs%285%2B1%29%3E=5-3
6%3E=2
TRUE. 1%3C=x also works.

The inequality seems to work for all values of x.