Question

Solve the equation. Check your solution.$\mathbf{21}\mathbf{=}\mathbf{4}\mathbf{x}\mathbf{-}\mathbf{9}\mathbf{-}\mathbf{x}$

Short answer

The solution for the equation $21=4x-9-x$is$x=10$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}21=4x-9-x\\ 21=3x-9\\ 21+9=3x-9+9\\ 30=3x\\ 3x=30\end{array}$

– Solve for x

Now, divide both sides of the equation by 10.

$\begin{array}{c}\frac{3x}{3}=\frac{30}{3}\\ x=10\end{array}$

Therefore, the solution of the equation is$x=10$.

– Check the solution 

To check the solution, write the original equation and substitute the value of x.$21=4x-9-x$

Now, substitute $x=10$and check the result.

$\begin{array}{c}21=4\left(10\right)-9-10\\ 21=40-9-10\\ 21=40-19\\ 21=21\end{array}$

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