How do you solve #|2.3 - 5.7x| = 11.4#?

1 Answer
Mar 13, 2018

Answer:

Find the solutions of x that give you #+-11.4# inside the absolute value bars. For that scenario, x=-1.5965 and x=2.4035

Explanation:

Because we're dealing with an absolute value, x can have two solutions since:

#abs(11.4)=11.4# and #abs(-11.4)=11.4#

Therefore, we need to find the following solutions:

#2.3-5.7x = 11.4#
#2.3-5.7x=-11.4#

The first step for both is to subtract 2.3 from both sides, and the second step is to divide by x's coefficient. This gives you the solution:

#x=(11.4-2.3)/(-5.7) rArr x=-9.1/5.7 = -1.5965#

#x=(-11.4-2.3)/(-5.7) rArr x=13.7/5.7 = 2.4035#