How do you solve #-2|-5x + 2| + 2 = -74#?

1 Answer
Feb 27, 2017

Answer:

#x = -7.2, 8#

Explanation:

Start rearranging the bits outside of the modulus:

#-2|-5x+2|+2 = -74#
#|-5x+2| = (-76)/(-2)=38#

A modulus is a positive or negative become positive. There are two ways to solve it.

Firstly, you can square both sides, because either positive or negative numbers squared become positive. However, #38^2# is a big number, so this is considerably more difficult than the second method.

Solve two equations, a positive and a negative.

1) #-5x+2=38#
2) #-5x+2=-38#

Now solve each:

1) #-5x+2=38#
#-5x = 36#
#x = -7.2#

2) #-5x+2=-38#
#-5x = -40#
#x = 8#

So now you have your solutions:

#x = -7.2, +8#