Question

How do you solve $\dfrac{16.5+3t}{3}=\dfrac{0.9-t}{-5}$?

Answer 1

Hint: The given equation looks complicated due to the fractions present in it. Therefore we must simplify the equation by cross multiplying the terms so as to obtain the equation \[-5\left( 16.5+3t \right)=3\left( 0.9-t \right)\]. Then we can simplify the equation by solving the brackets. For this we have to use the distributive rule of the algebraic multiplication, which is given by $a\left( b+c \right)=ab+ac$. Then finally, using the basic algebraic operations, we will obtain the required solution of the given equation.

Complete step-by-step answer:
The equation given in the above question is written as
$\Rightarrow \dfrac{16.5+3t}{3}=\dfrac{0.9-t}{-5}$
On cross multiplying the terms, we get
$\Rightarrow -5\left( 16.5+3t \right)=3\left( 0.9-t \right)$
Using the distributive law of the algebraic multiplication, which is given as $a\left( b+c \right)=ab+ac$, we can simplify the above equation as
$\begin{align}
  & \Rightarrow -5\left( 16.5 \right)-5\left( 3t \right)=3\left( 0.9 \right)-3t \\
 & \Rightarrow -82.5-15t=2.7-3t \\
\end{align}$
Adding $3t$ both the sides, we get
$\begin{align}
  & \Rightarrow -82.5-15t+3t=2.7-3t+3t \\
 & \Rightarrow -82.5-12t=2.7 \\
\end{align}$
Now, on adding $82.5$ both the sides, we get
$\begin{align}
  & \Rightarrow -82.5-12t+82.5=2.7+82.5 \\
 & \Rightarrow -12t=85.2 \\
\end{align}$
Finally, on dividing both the sides by $-12$, we get
$\begin{align}
  & \Rightarrow t=-\dfrac{82.5}{12} \\
 & \Rightarrow t=-6.875 \\
\end{align}$
Hence, the solution of the given equation is $t=-6.875$.

Note: We must check the final obtained solution by substituting it back into the given equation whether it satisfies it or not. This is because there are a lot of calculations involved in the solution of this question which invites chances of calculation errors. Do not forget the negative sign present before twelve in the obtained equation $-12t=85.2$. If we cannot understand the cross multiplication in one go, which is done in the above solution, then we can consider multiplying the given equation by the denominators of both the fractions, one by one.