How do you solve the equation #abs(3(x-2))=10#?

1 Answer
Nov 29, 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:

#color(red)(3)(x - 2) = -10#

#(color(red)(3) xx x) - (color(red)(3) xx 2) = -10#

#3x - 6 = -10#

#3x - 6 + color(red)(6) = -10 + color(red)(6)#

#3x - 0 = -4#

#3x = -4#

#(3x)/color(red)(3) = -4/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -4/3#

#x = -4/3#

Solution 1:

#color(red)(3)(x - 2) = 10#

#(color(red)(3) xx x) - (color(red)(3) xx 2) = 10#

#3x - 6 = 10#

#3x - 6 + color(red)(6) = 10 + color(red)(6)#

#3x - 0 = 16#

#3x = 16#

#(3x)/color(red)(3) = 16/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 16/3#

#x = 16/3#

The Solution Is: #x = {-4/3, 16/3}#