# How do you solve 1/4t-1/6=-4/9?

Jun 29, 2017

$t = - \frac{20}{18}$

#### Explanation:

First put the $\frac{1}{6}$ on the other side so that $t$ is on its own.

$\frac{1}{4} t = - \frac{4}{9} + \frac{1}{6}$

Find a common denominator, 18, so that the two fractions can be added together.

$\frac{1}{4} t = \frac{- 8 + 3}{18} \to - \frac{5}{18}$

$\frac{t}{4} = - \frac{5}{18}$

$18 t = - 20$

$t = - \frac{20}{18}$

Jun 29, 2017

$t = - \frac{10}{9}$

#### Explanation:

First, bring the constants (a number on its own) to the right-hand side in order to isolate $t$. We end up with $t$ on the left-hand side and the constants on the right-hand side. If we bring $- \frac{1}{6}$ over, we have to do the inverse operation. In this case, we do

$\frac{t}{4} - \frac{1}{6} = - \frac{1}{9}$
$\frac{t}{4} = - \frac{1}{9} + \frac{1}{6}$
$\frac{t}{4} = - \frac{5}{18}$

We can then cross multiply which is when we multiply the denominators and numerators that are diagonal to each other, like this:

$t \cdot 18 = - 5 \cdot 4$
$18 t = - 20$

All we have to do is to divide each side by 18 to get $t$ by itself.

$\frac{18 t}{18} = - \frac{20}{18}$
$t = - \frac{10}{9}$

Hope this helps you, mate.