Question

Solve the equation. Check your solution.

$\mathbf{25}\mathbf{t}\mathbf{=}\mathbf{5}\left(\mathbf{5}\mathbf{t}\mathbf{+}\mathbf{1}\right)$

Short answer

The equation $25t=5\left(5t+1\right)$ 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,

$\begin{array}{c}25t=5\left(5t+1\right)\\ 25t=25t+5\\ 25t-25t=25t+5-25t\left(\text{Subtract}25t\text{frombothsides}\right)\end{array}$

– Combine the like terms

Combine the like terms to get,

$0=5$.

– Conclusion 

Since 0 is not equal to 5, the equal $0=5$ is not true. Hence, there is no solution to the equation $25t=5\left(5t+1\right)$.