How do you solve $| x + 1 | = | - 4 x + 3 |$ $abs(x + 1)=abs(-4 x + 3)$ ?

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Answer 1 · 2018-05-25T11:18:16

The solutions are ${(x=4/3),(x=2/5):}$

The equation is

$|x+1|=|-4x+3|$

Removing one absolute value at a time :

$|x+1|=-4x+3$ and $|x+1|=4x-3$

The first equation gives

$|x+1|=-4x+3$

$<=>$ , ${(x+1=-4x+3),(-x-1=-4x+3):}$

$<=>$ , ${(5x=2),(3x=4):}$

$<=>$ , ${(x=2/5),(x=4/3):}$

The second equation gives

$|x+1|=4x-3$

$<=>$ , ${(x+1=4x-3),(-x-1=4x-3):}$

$<=>$ , ${(3x=4),(5x=2):}$

$<=>$ , ${(x=4/3),(x=2/5):}$

graph{(y-|x+1|)(y-|-4x+3|)=0 [-6.38, 7.67, -1.74, 5.283]}

How do you solve abs(x + 1)=abs(-4 x + 3)|x+1|=|−4x+3|abs(x + 1)=abs(-4 x + 3)?