Question

Solve the equation. Check your solution.

$\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{6}\mathbf{=}\mathbf{3}\left(\mathbf{x}\mathbf{+}\mathbf{2}\right)$

Short answer

The solution for the equation $3x+6=3\left(x+2\right)$ is all real numbers.

Step-by-step solution

– Use distributive property

The distributive property is given as $a\left(b+c\right)=ab+ac$.

The given equation is $3x+6=3\left(x+2\right)$.

So,

$\begin{array}{c}3x+6=3\left(x+2\right)\\ 3x+6=3x+6\left(\text{Usedistributiveproperty}\right)\end{array}$

– Combine the like terms

Combine the like terms.

$\begin{array}{c}3x-3x+6=3x-3x+6\left(\text{subtract3xfrombothsides}\right)\\ 0+6=0+6\\ 6=6\end{array}$

Since $6=6$ is true, the solution of the equation are all real numbers.

– Check the solution

To check the solution, choose any real number as a value of x and substitute in the equation $3x+6=3\left(x+2\right)$.

Choose $x=1$.

Then, substitute $x=1$ in $3x+6=3\left(x+2\right)$ and check the result.

$\begin{array}{c}3\times 1+6=3\left(1+2\right)\\ 3+6=3\times 3\\ 9=9\end{array}$

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