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Q8.

Expert-verified
Found in: Page 127

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

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

See the step by step solution

Step 1. Separate the variable and constants

Write the original equation and separate the variable and constants.

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

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 of x.

$5+2\left(x-2\right)=19$

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

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

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