Question

Solve the equation. Check your solution.

$\mathbf{8}\mathbf{v}\mathbf{=}\mathbf{2}\left(\mathbf{4}\mathbf{v}\mathbf{+}\mathbf{2}\right)$

Short answer

The equation $8v=2\left(4v+2\right)$ has no solution.

Step-by-step solution

– Use distributive property

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

The given equation is $25t=25t+5$.

So,

$\begin{array}{c}8v=2\left(4v+2\right)\\ \frac{8v}{2}=\frac{2\left(4v+2\right)}{2}\left(\text{divideeachsideby2}\right)\\ 4v=4v+2\left(\text{simplify}\right)\end{array}$

– Combine the like terms

Combine the like terms.

$\begin{array}{c}4v-4v=4v-4v+2\left(\text{subtract4vfrombothsides}\right)\\ 0=2\left(\text{simplify}\right)\end{array}$

– Conclusion 

Since 0 is not equal to 2, the equal $0=2$ is not true. Hence, there is no solution to the equation $8v=2\left(4v+2\right)$.