5. Cross multiplication method

  

The cross multiplication method is one of the methods to solve an equation. If the given equation is not in a linear polynomial form, we use the cross multiplication method of solving.

 

Let's understand this concept with an example.

 

 

The given equation is $\frac{2x+4}{2}=\frac{x+4}{10}$. This is not in linear polynomial form and also the equation contains variable on both sides. Now apply the cross multiplication rule in this equation.

 

 

Multiply the numerator in LHS $(2x+4)$ by the denominator in RHS $(10)$.

 

That is $10(2x+4)$.

 

 

Multiply the RHS numerator $x+4$ by the LHS denominator $2$.

 

That is $2(x+4)$.

 

These steps are explained in the figure given below.

 

 

 

Simplify both the sides of the equation.

 

 

 

Now transpose the $40$ to $RHS$ side and transpose the variable $2x$ in $RHS$ to $LHS$.

 

 

 

Now use the linear equation rule. That is divide by 18 on both sides of the equation.

 

Therefore the solution for the equation $\frac{2x+4}{2}=\frac{x+4}{10}$ is $x = -2$.