Question

How do you solve $\dfrac{3}{4}n=-1\dfrac{3}{4}n-18$?

Answer 1

We separate the variables and the constants of the equation $\dfrac{3}{4}n=-1\dfrac{3}{4}n-18$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of $n$.

Complete step by step solution:
The given equation $\dfrac{3}{4}n=-1\dfrac{3}{4}n-18$ is a linear equation of $n$. we need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $\dfrac{3}{4}n+1\dfrac{3}{4}n+18=0$ are either variable of $n$ or a constant. We first separate the variables and the constants. We know $1\dfrac{3}{4}=\dfrac{7}{4}$.
We take the variables to get $\dfrac{3}{4}n,\dfrac{7}{4}n$.
The binary operation of addition gives $\dfrac{3}{4}n+\dfrac{7}{4}n=\dfrac{7+3}{4}n=\dfrac{10}{4}n$.
We take the constants all together. There is one such constant which is 18.
The binary operation of addition gives us $\dfrac{10}{4}n+18=0$ which gives $\dfrac{10}{4}n=-18$.
Now we simplify the equation to get

& \dfrac{10}{4}n=-18 \\\ & \Rightarrow n=\dfrac{\left( -18 \right)\times 4}{10} \\\ & \Rightarrow n=-\dfrac{36}{5} \\\ \end{aligned}$$ **Therefore, the final solution becomes $$n=-\dfrac{36}{5}$$.** **Note:** We can verify the result of the equation $$\dfrac{3}{4}n=-1\dfrac{3}{4}n-18$$ by taking the value of as $$n=-\dfrac{36}{5}$$. Therefore, the left-hand side of the equation becomes $\dfrac{3}{4}n=\dfrac{3}{4}\times \left( -\dfrac{36}{5} \right)=-\dfrac{27}{5}$. The right-hand side of the equation becomes $-1\dfrac{3}{4}n-18=-\dfrac{7}{4}\times \left( -\dfrac{36}{5} \right)-18=\dfrac{63}{5}-18=n=-\dfrac{27}{5}$. Thus, verified for the equation $$\dfrac{3}{4}n=-1\dfrac{3}{4}n-18$$ the solution is $$n=-\dfrac{36}{5}$$.