# Teacher told to set absolute value inequality to equal 0

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1. Mar 25, 2015

### asadpasat

So I was helping my sister on homework and there was this problem:
2 abs(2x + 4) +1 > or equal to -3
teacher told her to ignore the -3 and just set it equal to zero.
Soo should you? This question got me confused. can't you just go about solving, bringing the 1 to the left and then dividing by 2?
EDIT: when I do it I get interval notaion from -3 to 3
and with the zero thing i get -2.5 to 2.5

Last edited: Mar 25, 2015
2. Mar 25, 2015

### Staff: Mentor

$2|2x + 4| + 1 \ge -3$
$\Leftrightarrow 2|2x + 4| \ge -4$
$\Leftrightarrow |2x + 4| \ge -2$
Since the absolute value is always greater than or equal to zero, you can change the last inequality to $|2x + 4| \ge 0$.

3. Mar 25, 2015

### mathman

|anything|≥0. Therefore 2|2x+4|+1≥1 for all x. Any x will do.

4. Mar 25, 2015

### HallsofIvy

Staff Emeritus
Your teacher's point is that "f(x)= 0", for f a continuous function, is the boundary beween "f(x)> 0" and "f(x)< 0".

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