Question

Solve the equation. Check your solution.

$\mathbf{8}\mathbf{a}\mathbf{-}\mathbf{2}\left(\mathbf{a}\mathbf{+}\mathbf{5}\right)\mathbf{=}\mathbf{2}\left(\mathbf{a}\mathbf{-}\mathbf{1}\right)$

Short answer

The solution for the equation $8a-2\left(a+5\right)=2\left(a-1\right)$ is $a=2$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}8a-2\left(a+5\right)=2\left(a-1\right)\\ 8a-2a-10=2a-2\left(\text{Simplify}\right)\\ 6a-10=2a-2\\ 6a-10-2a=2a-2a-2\left(\text{Subtract2afrombothsides}\right)\\ 4a-10=-2\left(\text{Simplify}\right)\\ 4a-10+2=-2+2\left(\text{Add2tobothsides}\right)\\ 4a-8=0\left(\text{Simplify}\right)\end{array}$

– Solve for a

Now, divide both sides of the equation by 4.

$\begin{array}{c}\frac{4a}{4}=\frac{8}{4}\\ a=2\end{array}$

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.

$8a-2\left(a+5\right)=2\left(a-1\right)$

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

$\begin{array}{c}8\times 2-2\left(2+5\right)=2\left(2-1\right)\\ 16-2\left(7\right)=2\times 1\\ 16-14=2\\ 2=2\end{array}$

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