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

1 Answer
Tony B
Apr 23, 2017

#x=-3 and x=11#

Explanation:

The two vertical lines used this way are a special sort of brackets and they signify an 'Absolute' value. That is; whatever is between those lines is always considered as positive

So if the answer is positive 7 then what is inside those special brackets can only end up as two values. These are #+-7# in that:

#|+-7|=+7#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the case #4-x=-7#

Multiply both sides by (-1) #-># changes #-x# to #+x#

#-4+x=+7#

Add 4 to both sides #-># get rid of the -4 on the left

#-4+4+x=4+7#

#0+x=+11#

So one value is #x=11#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the case #4-x=+7#

Multiply by (-1)

#-4+x=-7#

So the other value is #x=-3#

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