Question

Solve the following equation: $\frac{3y+4}{2-6y}=\frac{-2}{5}$

Answer 1

Solve linear equations in one variable.

Step 1: Cross-multiply to form a linear equation.

$\begin{array}{rcl}\frac{3y+4}{2-6y}& =& \frac{-2}{5}\\ & \Rightarrow & 5\left(3y+4\right)=-2\left(2-6y\right)\\ & \Rightarrow & 15y+20=-4+12y\end{array}$

Step 2: Transpose $20$ to RHS and $12y$ to LHS of the equation.

$\begin{array}{rcl}15y-12y& =& -4-20\\ & \Rightarrow & 3y=-24\end{array}$

Step 3: Divide both sides by $3$.

$\begin{array}{rcl}\frac{3y}{3}& =& \frac{-24}{3}\\ & \Rightarrow & y=-8\end{array}$

Hence, the solution of the equation $\frac{3y+4}{2-6y}=\frac{-2}{5}$ is $y=-8$.