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Answers without the blur. Sign up and see all textbooks for free! Q21.

Expert-verified Found in: Page 133 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Solve the equation. Check your solution.$\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{6}\mathbf{=}\mathbf{3}\left(\mathbf{x}\mathbf{+}\mathbf{2}\right)$

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

See the step by step solution

## Step 1 – 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,

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

## Step 2 – Combine the like terms

Combine the like terms.

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

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

## Step 3 – 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.

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

As the left-hand side is equal to right hand side, this signifies that the solution is correct. ### Want to see more solutions like these? 