Question

Solve each equation. Check your solution.

$\frac{3}{11}a-1=\frac{7}{11}a+9$

Short answer

The required answer is $-\frac{55}{2}$.

Step-by-step solution

Step 1- Isolate the variable a

Perform addition of 1 and subtraction of $\frac{7}{11}a$ on both the sides of the equation.

$\begin{array}{c}\frac{3}{11}a-1+1-\frac{7}{11}a=\frac{7}{11}a+9+1-\frac{7}{11}a\\ -\frac{4}{11}a=10\end{array}$

Perform division of$-\frac{4}{11}$ on both the sides of the equation

$\begin{array}{c}\frac{-\frac{4}{11}a}{-\frac{4}{11}}=\frac{10}{-\frac{4}{11}}\\ a=-\frac{55}{2}\end{array}$

– Check the obtained value 

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

$\begin{array}{l}\frac{3}{11}\left(-\frac{55}{2}\right)-1\stackrel{?}{=}\frac{7}{11}\left(-\frac{55}{2}\right)+9\\ -\frac{15}{2}-1\stackrel{?}{=}-\frac{35}{2}+9\\ -\frac{17}{2}=-\frac{17}{2}\end{array}$

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.