Question

How do you solve $2\dfrac{5}{12}=-3\dfrac{1}{4}+k$?

Answer 1

Hint: Now we are given with a linear equation in k. To solve the equation we will first convert mixed fractions into simple fractions. Now we will take the LCM of denominators and multiply the equation with it to eliminate the fractions. Now we will simplify the equation to find the value of k.

Complete step by step answer:
Now consider the given equation $2\dfrac{5}{12}=-3\dfrac{1}{4}+k$
Now the given equation is a linear equation in one variable. Now we want to solve the given equation. Hence we want to find the value of k for which the equation holds.
Now we can see that the coefficients of the equation are not integers so we will first try to convert them into integers.
Now first let us solve the mixed fraction in the equation. We know that $a\dfrac{b}{c}=\dfrac{ac+b}{c}$ . Hence using this we get,
\[\begin{align}
  & \Rightarrow \dfrac{12\times 2+5}{12}=\dfrac{-3\times 4+1}{4}+k \\
 & \Rightarrow \dfrac{24+5}{12}=\dfrac{-12+1}{4}+k \\
 & \Rightarrow \dfrac{29}{12}=\dfrac{-11}{4}+k \\
\end{align}\]
Now let us eliminate the fractions by multiplying the whole equation by LCM of denominators.
Now the LCM of 12 and 4 is 12. Hence multiplying the whole equation by 12 we get,
$\begin{align}
  & \Rightarrow 29=-11\left( 3 \right)+12k \\
 & \Rightarrow 29=-33+12k \\
\end{align}$
Now adding 33 on both sides of the equation we get,
$\Rightarrow 29+33=33-33+12k$
Hence we get the value of k = 62/12=31/6.

Hence the solution of the given equation is k = 31/6.

Note: Now note that the mixed fraction written as $2\dfrac{3}{5}$ is $2+\dfrac{3}{5}$ and not $\dfrac{2\times 3}{5}$ . Hence take care while solving mixed fractions. Also always check the solution by re-substituting the value of the variable into the equation.