How do you solve the equation #abs(ax)=b#?

1 Answer
smendyka
Aug 9, 2017

Assuming the solution being requested is for #x#, see a solution process below:

Explanation:

The absolute value function takes any negative or positive 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

#ax = -b#

#(ax)/color(red)(a) = -b/color(red)(a)#

#(color(red)(cancel(color(black)(a)))x)/cancel(color(red)(a)) = -b/a#

#x = -b/a#

Solution 2

#ax = b#

#(ax)/color(red)(a) = b/color(red)(a)#

#(color(red)(cancel(color(black)(a)))x)/cancel(color(red)(a)) = b/a#

#x = b/a#

The Solutions Are: #x = -b/a# and #x = b/a#

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