How do you solve #|-7x + 7| = 14#?

2 Answers
Deepak G.
Aug 4, 2016

#x=-1#
#x=3#

Explanation:

#-7x+7=14#
or
#-7x=14-7#
or
#-7x=7#
or
#x=-7/7#
or
#x=-1#................Ans#1#

Now consider
#-7x+7=-14#
or
#-7x=-14-7#
or
#-7x=-21#
or
#7x=21#
or
#x=21/7#
or
#x=3#.....................Ans#2#

Tony B
Aug 4, 2016

#x= -1" and "x=3" "# are solutions

Explanation:

Remember that everything inside the two | | is read as positive. This is called an 'absolute' value

Written as in the question or as 'abs(-7x+7)=14'

Tony B

#color(brown)("Observe where the red and blue lines cross. It is evident that this")# #color(brown)("expression gives two values for "x" as an answer.")#

The part of the equation inside the | | may be positive or negative but will always be read as a final positive overall value.

Thus what is inside the | | has the possibility to be -14 or +14 and still satisfy the equation

Suppose #-7x+7=14#

#color(blue)("Then "-7x=7" " =>" " x=(-1))#

Suppose #-7x+7=-14#

#color(blue)("Then "-7x=-21" "=>" "x=3)#

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