How do you solve |16+t|=2t−3?

1 Answer
Jothi S.
Aug 3, 2016

t=19

Explanation:

|16+t|=2t−3

|x|is distance from the origin
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(16+t)=2t−3or−(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=−133

plugt=19 in the original equation
|16+19|=2(19)−3
|35|=35

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

Put t=-13/3 in the original equation
∣∣∣16−(133)∣∣∣=2(−133)−3
∣∣∣48−133∣∣∣=−(263)−3
∣∣∣353∣∣∣=−26−93
353=−353Left 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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