How do you solve # |16 + t| = 2t - 3#?

1 Answer
Aug 3, 2016

Answer:

t=19

Explanation:

#abs(16+t)=2t-3#

#abs(x) #is distance from the origin
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# (16+t)=2t-3 or -(16t+t)=2t-3#
Take # (16+t)=2t-3 #
#16+3=2t-t#
#19=t#
#t=19#
Take #(16+t)=-(2t-3)#
#16+t=-2t+3#
#16-3=-2t-t#
#13=-3t#
#t=-13/3#

# plug t=19# in the original equation
#abs(16+19)=2(19)-3#
#abs(35)=35#

#35=35#
So t=19 satisfies the original equation.

Put t=-13/3 in the original equation
#abs(16-(13/3))=2(-13/3)-3#
#abs ((48-13)/3)=-(26/3)-3#
#abs(35/3)=(-26-9)/3#
#35/3=-35/3#Left and right hand side are not same
so t=-13/3 should not satisfies the original equation
so it is extraneous solution.
t=19