Question

Solve each equation. Check your solution.

$-\frac{3}{4}n+1=-11$

Short answer

The required answer is 16.

Step-by-step solution

Step 1- Isolate the variable n

Perform subtraction of 1 from both the sides of the equation.

$\begin{array}{c}-\frac{3}{4}n+1-1=-11-1\\ -\frac{3}{4}n=-12\end{array}$

Perform division of $-\frac{3}{4}$ from both the sides of the equation.

$\begin{array}{c}\frac{-\frac{3}{4}n}{-\frac{3}{4}}=\frac{-12}{-\frac{3}{4}}\\ -\frac{4}{3}\left(-\frac{3}{4}n\right)=\left(-12\right)\cdot -\frac{4}{3}\\ n=16\end{array}$

– Check the obtained value 

Substitute the obtained value of n into the original equation and perform simplification for checking.

$\begin{array}{l}-\frac{3}{4}\left(16\right)+1\stackrel{?}{=}-11\\ -12+1\stackrel{?}{=}-11\\ -11=-11\end{array}$

Step 3- Make the conclusion

As the checking results in equal values on both the sides on substation of obtained value which means that obtained value is correct.