Question

Solve the following equation: $3\left(t-3\right)=5\left(2t+1\right)$.

Answer 1

Solve linear equations in one variable.

Step 1: Open the brackets on both sides.

$\begin{array}{rcl}3\left(t-3\right)& =& 5\left(2t+1\right)\\ & \Rightarrow & 3t-9=10t+5\end{array}$

Step 2: Add $9$ to both sides of the equation.

$\begin{array}{rcl}3t-9+9& =& 10t+5+9\\ & \Rightarrow & 3t=10t+14\end{array}$

Step 3: Transpose $10t$ to LHS.

$$\begin{gathered} 3t-10t=14 \\ \Rightarrow -7t=14 \end{gathered}$$

Step 4: Divide both sides by $-7$.

$\begin{array}{rcl}\frac{-7t}{-7}& =& \frac{14}{-7}\\ & \Rightarrow & t=-2\end{array}$

Hence, the solution of the equation $3\left(t-3\right)=5\left(2t+1\right)$ is $t=-2$.