Question

Solve the equation. Check your solution.

$\mathbf{5}\mathbf{+}\mathbf{2}(\mathbf{x}\mathbf{-}\mathbf{2})\mathbf{=}\mathbf{19}$

Short answer

The solution for the equation $5+2(x-2)=19$is$x=9$.

Step-by-step solution

Step 1. Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}5+2(x-2)=19\\ 5+2x-4=19\\ 2x+1=19\\ 2x-1+1=19-1\\ 2x=18\end{array}$

Step 2. Solve for x

Now, divide both sides of the equation by 2.

$\begin{array}{c}\frac{2x}{2}=\frac{18}{2}\\ x=9\end{array}$

Therefore, the solution of the equation is $x=9$.

Step 3. Check the solution 

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

$5+2(x-2)=19$

Now, substitute $x=9$and check the result.

$\begin{array}{c}5+2(9-2)=19\\ 5+2\left(7\right)=19\\ 5+14=19\\ 19=19\end{array}$

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