How do you solve #|t - 6| = 4#?

2 Answers
Shwetank Mauria
Dec 22, 2016

#t=2# or #t=10#

Explanation:

#|k|# stands for absolute value of #k#, which is the numerical value of #k# sans its sign. So while the absolute value of #7# is #7#, absolute value of #|-7|# too is #7#.

In short, if #k# is positive #|k|=k#, but if #k# is negative #|k|=-k#.

Thus while #|7|=7#, #|-7|=-(-7)=7#.

Hence, as we have #|t-6|=4#

either #|t-6|=4#

i.e. #t-6=4# i.e. #t=6+4=10#

or #-(t-6)=4#

i.e. #-t+6=4# i.e. #6-4=t# i.e. #t=2#

#.:t=2# or #t=10#.

Meave60
Dec 22, 2016

#t=10# or #t=2#

Explanation:

#abs(t-6)=4# or #abs(t-6)=-4#

#abs(t-6)=4#

#t-6=4#

Add #6# to both sides.

#t=10#

#color(red)(..................)#

#abs(t-6)=-4#

#t-6=-4#

Add #6# to both sides.

#t=2#

#t=10# or #t=2#

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