# How do you solve |x+ 30|= 4x?

Apr 11, 2018

x = 10

#### Explanation:

1. we have to find, when the absolute value (ABS) is more than zero and when less
zero point for this ABS is x=-30
2. then we will solve this problem for 2 intervals, one interval when ABS is possitive and one when ABS is negative

first interval:
(in this interval ABS is negative therefore we write -(x+30) instead of ABS)
x in (-oo;-30): -(x+30)=4x
$- 30 = 5 x$
$x = - 6$
but -6!in(-oo;-30) => x=-6 "is not solution"

second interval:
(in this interval ABS is possitive therefore we write (x+30) instead of ABS)
x in (-30;oo): (x+30)=4x
$30 = 3 x$
$x = 10$
10in(-30;oo) => x=10 "is solution"