# How do you solve 5= \frac { 9+ t } { 4}?

Jan 27, 2017

$t = 11$.

#### Explanation:

$5 = \frac{9 + t}{4}$

Mulitply BOTH sides by $4$.

$5 \times 4 = \frac{9 + t}{\cancel{4}} \times \cancel{4} = 20 = 9 + t$

Subtract $9$ FROM BOTH SIDES:

$20 - 9 = \cancel{9} + t - \cancel{9}$

$t = 11$

All I have done here is to manipulate BOTH sides of the equality equivalently. What I did to one side, I must do to the other.

Jan 27, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{4}$ to eliminate the fraction and to keep the equation balanced.

$5 \times \textcolor{red}{4} = \frac{9 + t}{4} \times \textcolor{red}{4}$

$20 = \frac{9 + t}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} \times \cancel{\textcolor{red}{4}}$

$20 = 9 + t$

Now, subtract $\textcolor{red}{9}$ from each side of the equation to solve for $t$ while keeping the equation balanced:

$20 - \textcolor{red}{9} = 9 + t - \textcolor{red}{9}$

$11 = 9 - \textcolor{red}{9} + t$

$11 = 0 + t$

$11 = t$

$t = 11$