Question

Solve the equation. Check your solution.

$\mathbf{9}\mathbf{+}\mathbf{2}\mathbf{x}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{2}$

Short answer

The solution for the equation $9+2x=3x-2$ is $x=11$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}9+2x=3x-2\\ 9+2x-2x=3x-2x-2\left(\text{Subtract2xfrombothsides}\right)\\ 9=x-2\left(\text{Simplify}\right)\end{array}$

– Solve for x

$\begin{array}{c}9+2=x-2+2\left(\text{Add2tobothsides}\right)\\ x=11\left(\text{Simplify}\right)\end{array}$

Therefore, the solution of the equation is $x=11$.

– Check the solution 

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

$2\left(-4h-13\right)=37+13h$

Now, substitute $x=11$ and check the result.

$\begin{array}{c}9+2\times 11=3\times 11-2\\ 9+22=33-2\\ 31=31\end{array}$

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