Question

Solve each equation. Check your solution.

$\mathbf{5}\mathbf{t}\mathbf{-}\mathbf{3}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{t}\mathbf{+}\mathbf{10}$

Short answer

The solution of the given equation is $\frac{\mathbf{13}}{\mathbf{7}}$.

Step-by-step solution

– Description of step.

Add 3 on both the sides of the given equation.

$\begin{array}{c}5t-3+3=-2t+10+3\\ 5t=-2t+13\end{array}$

– Description of step.

Add $2t$ on both the sides of the obtained equation in step 1.

$\begin{array}{c}5t+2t=-2t+13+2t\\ 7t=13\end{array}$

– Description of step.

Divide each side of the equation in step 2.

$\begin{array}{c}\frac{7t}{7}=\frac{13}{7}\\ t=\frac{13}{7}\end{array}$

– Description of step.

To check whether the obtained value of $t$is the solution of given equation, substitute $\frac{13}{7}$for $t$ into $5t-3=-2t+10$and simplify.

$\begin{array}{c}5\left(\frac{13}{7}\right)-3=-2\left(\frac{13}{7}\right)+10\\ \frac{65}{7}-3\stackrel{?}{=}\frac{-26}{7}+10\\ \frac{44}{7}\stackrel{?}{=}\frac{44}{7}\\ \frac{44}{7}=\frac{44}{7}\end{array}$

Therefore, the solution of the given equation is $\frac{13}{7}$.