SOLUTION: Can you please help me solve this absolute value inequality?? :) | 2x + 1 | + | x - 4 | > 0 my calculations are : |2x + 1| + |x - 4|>0 |2x+1|>-|x-4| square both sides 4x^2 +

Question 447772: Can you please help me solve this absolute value inequality?? :)
| 2x + 1 | + | x - 4 | > 0
my calculations are :
|2x + 1| + |x - 4|>0
|2x+1|>-|x-4|
square both sides
4x^2 + 4x + 1 > x^2 - 8x + 16
...3x^2 + 12x - 15 > 0
(3x+15)(x-1)>0
i use quadratic curve and got x<5 , x>1

Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Consider this: |2x + 1| > 0 for all real values of x except x = -1/2. And |x - 4| > 0 for all x except x = 4. So the sum of these two expressions is ALWAYS greater than zero. The inequality is true for all real values of x.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You are over-thinking the problem, and with that solution, you are likely to make a mistake, since you cannot directly assume you can square both sides with the absolute value signs.

Just note that you have a sum of two absolute value expressions, and the absolute value of any quantity is nonnegative. |2x+1| > 0 unless x = -1/2, and |x-4| > 0 unless x = 4. Since x cannot be -1/2 and 4 at the same time, at least one of the absolute value expressions must be greater than 0, so the inequality holds for all real numbers x.
RELATED QUESTIONS
can you please help me solve this equation, 2x-y+1=0 and... (answered by Alan3354)
Example: Please help me solve this equation: {{{ x^4+2x^3-2x-1=0... (answered by stanbon)
Example: Please help me solve this equation: {{{ x^4+2x^3+3x^2+2x+1=0... (answered by stanbon,Edwin McCravy)
can you please show me how to solve this absolute value equation and inequality?... (answered by stanbon)
Can you please help me to solve this equation:... (answered by edjones)
please help me solve this equation: {{{ x^+2x+4=0... (answered by Alan3354)
Can you please help me solve this problem?... (answered by Edwin McCravy)
I need help with this inequality. Can you please solve this for me:... (answered by mananth)
Can you please help me with this equation? Calculate the value of the discriminant of... (answered by Alan3354)