SOLUTION: Solve: abs(2x+1)+1<=8 Solving the absolute value I get -5<=x<=8, but my calculator gives me -4<=x<=8

Algebra ->  Absolute-value -> SOLUTION: Solve: abs(2x+1)+1<=8 Solving the absolute value I get -5<=x<=8, but my calculator gives me -4<=x<=8       Log On


   

Question 1084597: Solve: abs(2x+1)+1<=8
Solving the absolute value I get -5<=x<=8, but my calculator gives me -4<=x<=8
Found 3 solutions by josgarithmetic, MathLover1, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
abs(2x+1)+1<=8
abs%282x%2B1%29%2B1%3C=8

-
abs%282x%2B1%29%3C=7

Either 2x%2B1%3E=0 or 2x%2B1%3C0.

NON-NEGATIVE
2x%2B1%3C=7
2x%3C=6
x%3C=3

NEGATIVE CASE
-2x-1%3C=7
-2x%3C=8
x%3E=-4

SOLUTION: highlight%28-4%3C=x%3C=3%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282x%2B1%29%2B1%3C=8
abs%282x%2B1%29%3C=8-1...recall that abs%282x%2B1%29=sqrt%282x%2B1%29; so, you have 2x%2B1 and -%282x%2B1%29
then,
2x%2B1%3C=7
2x%3C=7-1
2x%3C=6
x%3C=6%2F2
x%3C=3
or
-%282x%2B1%29%3C=7
-2x-1%3C=7
-7-1%3C=2x
-8%3C=2x
-8%2F2%3C=x
-4%3C=x


solution:
-4%3C=x%3C3

postimage




Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
|2x+1| + 1 <= 8
-----
|2x+1| <= 7
2x+1 <= 7
x <= 3
-------------
-(2x+1) <= 7
-2x <= 8
-x <= 4
0 <= x+4
-4 <= x
=====================
-4 <= x <= 3