Question

Solve the equation. Check your solution.

$\mathbf{14}\mathbf{a}\mathbf{-}\mathbf{93}\mathbf{=}\mathbf{49}\mathbf{-}\mathbf{57}\mathbf{a}$

Short answer

The solution for the equation $14a-93=49-57a$ is $a=2$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}14a-93=49-57a\\ 14a+57a-93=49-57a+57a\left(\text{add57atobothsides}\right)\\ 71a-93=49\left(\text{simplify}\right)\\ 71a-93+93=49+93\left(\text{add93tobothsides}\right)\\ 71a=142\left(\text{simplify}\right)\end{array}$

– Solve for a

Now, divide both sides of the equation by 71.

$\begin{array}{c}\frac{71a}{71}=\frac{142}{71}\\ a=2\end{array}$

Therefore, the solution of the equation is $a=2$.

– Check the solution 

To check the solution, write the original equation and substitute the value of a.

$14a-93=49-57a$

Now, substitute $a=2$ and check the result.

$\begin{array}{c}14\times 2-93=49-57\times 2\\ 28-93=49-114\\ -65=-65\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.