How do you solve #|- 7x - 1| = 50#?

1 Answer
Apr 16, 2018

#x\in{-51/7; 7}#

Explanation:

We have:

#|-7x-1|=50#

If the absolute value of an expression is equal to a certain quantity, then the expression's value must either equal the quantity itself or its opposite. Therefore, we can deduce that:

#-7x-1\in{-50;50}#

#-(7x+1)\in{-50;50}#

Multiplying both sides by #-1#:

#7x+1\in{-50; 50}#

Subtracting #1# and dividing by #7#:

#x\in{(-50-1)/7;(50-1)/7}#

#x\in{-51/7; 7}#