Question

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

Answer 1

t=19

Explanation:

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

`abs(x)`is distance from the origin

`(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