# Math Help - What am I doing wrong,inequalitie again

1. ## What am I doing wrong,inequalitie again

Solve following:
$Ix-4I+2x<7$
Those I:s mean absolute value...
Well I did this..

$(-7) $/+4$
$(-3)<3x<11$ $/ /3$
$(-1) but that is apparently very wrong...correct answer is x<3
Any idea where I wen´t wrong?

2. Originally Posted by Henryt999
Solve following:
$Ix-4I+2x<7$
Those I:s mean absolute value...
Well I did this..

$(-7) $/+4$
This is wrong, you should've done this: $|x-4|<7-2x\implies 2x-7 and solve each one separately.

By the way, can't you generate the | ?

3. Originally Posted by Henryt999
Solve following:
$Ix-4I+2x<7$
Those I:s mean absolute value...
Well I did this..

$(-7) $/+4$
$(-3)<3x<11$ $/ /3$
$(-1) but that is apparently very wrong...correct answer is x<3
Any idea where I wen´t wrong?
You can use the | key to mark the beginning and end of the modulus. On an English (UK) keyboard it's assigned to Shift+\ which is in the bottom left, next to shift.

$|x-4| + 2x < 7$

$|x-4| < 7 - 2x$

$\pm (x-4) < 7-2x$

A)
$(x-4) < 7-2x$

$3x < 11$

$x < \frac{11}{3}$

B)
$-(x-4) < 7-2x$

Multiply by $-1$: $(x-4) > 2x-7$

Collect like terms: $-x > -3$

Multiply by -1: $x < 3$

Since $3 < \frac{11}{3}$ discard solution A.