Question

Solve the equation. Check your solution.

$\mathbf{7}\left(\mathbf{2}\mathbf{p}\mathbf{+}\mathbf{1}\right)\mathbf{=}\mathbf{14}\mathbf{p}\mathbf{+}\mathbf{7}$

Short answer

The solution for the equation $7\left(2p+1\right)=14p+7$ 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 $7\left(2p+1\right)=14p+7$.

So,

$\begin{array}{c}7\left(2p+1\right)=14p+7\\ 14p+7=14p+7\left(\text{Usedistributiveproperty}\right)\end{array}$

– Combine the like terms

Combine the like terms.

$\begin{array}{c}14p-14p+7=14p-14p+7\left(\text{subtract14pfrombothsides}\right)\\ 7-7=0+7-7\left(\text{subtract7frombothsides}\right)\\ \text{0}=0\left(\text{simplify}\right)\end{array}$

Since $\text{0}=0$ 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 p and substitute in the equation $7\left(2p+1\right)=14p+7$.

Choose $p=2$.

Then, substitute $p=2$ in $7\left(2p+1\right)=14p+7$ and check the result.

$\begin{array}{c}7\left(2\times 2+1\right)=14\times 2+7\\ 7\left(4+1\right)=28+7\\ 7\times 5=28+7\\ 35=35\end{array}$

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