How do you solve #abs(4x-7)=13#?

1 Answer
Aug 22, 2017

Answer:

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

#4x - 7 = -13#

#4x - 7 + color(red)(7) = -13 + color(red)(7)#

#4x - 0 = -6#

#4x = -6#

#(4x)/color(red)(4) = -6/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -6/4#

#x = -3/2#

Solution 2:

#4x - 7 = 13#

#4x - 7 + color(red)(7) = 13 + color(red)(7)#

#4x - 0 = 20#

#4x = 20#

#(4x)/color(red)(4) = 20/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 5#

#x = 5#

The Solutions Are: #x = -3/2# and #x = 5#