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

Aug 3, 2016

t=19

#### Explanation:

$\left\mid 16 + t \right\mid = 2 t - 3$

$\left\mid x \right\mid$is distance from the origin

$\left(16 + t\right) = 2 t - 3 \mathmr{and} - \left(16 t + t\right) = 2 t - 3$
Take $\left(16 + t\right) = 2 t - 3$
$16 + 3 = 2 t - t$
$19 = t$
$t = 19$
Take $\left(16 + t\right) = - \left(2 t - 3\right)$
$16 + t = - 2 t + 3$
$16 - 3 = - 2 t - t$
$13 = - 3 t$
$t = - \frac{13}{3}$

$p l u g t = 19$ in the original equation
$\left\mid 16 + 19 \right\mid = 2 \left(19\right) - 3$
$\left\mid 35 \right\mid = 35$

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

Put t=-13/3 in the original equation
$\left\mid 16 - \left(\frac{13}{3}\right) \right\mid = 2 \left(- \frac{13}{3}\right) - 3$
$\left\mid \frac{48 - 13}{3} \right\mid = - \left(\frac{26}{3}\right) - 3$
$\left\mid \frac{35}{3} \right\mid = \frac{- 26 - 9}{3}$
$\frac{35}{3} = - \frac{35}{3}$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