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

1 Answer
Jothi S.
Aug 3, 2016

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=-35/3Left and right hand side are not same
so t=-13/3 should not satisfies the original equation
so it is extraneous solution.
t=19

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