Question

Solve the equation. Check your solution.$\mathbf{2}\mathbf{=}\mathbf{4}(\mathbf{3}\mathbf{k}\mathbf{-}\mathbf{8})\mathbf{-}\mathbf{11}\mathbf{k}$

Short answer

The solution for the equation $2=4(3k-8)-11k$is$k=34$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}2=4(3k-8)-11k\\ 2=12k-32-11k\left[\text{distributiveproperty}\right]\\ 2=k-32\left[\text{combineliketerms}\right]\end{array}$

– Solve for k

$\begin{array}{c}2+32=k-32+32\left[\text{add32toeachside}\right]\\ \begin{array}{c}34=k\left[\text{simplify}\right]\\ k=34\end{array}\end{array}$

Therefore, the solution of the equation is$k=34$.

– Check the solution 

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

$2=4(3k-8)-11k$

Now, substitute $k=34$and check the result.

$\begin{array}{c}2=4(3\times 34-8)-11\times 34\\ 2=4(102-8)-374\\ 2=4\left(94\right)-374\\ 2=376-374\\ 2=2\end{array}$

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