Chapter 7.4, Problem 4ST

To determine

To calculate: The solution of the equations.

  $\frac{m+6}{10}-\frac{m}{15}=\frac{2}{5}$ .

Answer to Problem 4ST

The solution of the equations is $m=-6$ .

Explanation of Solution

Given information:

The equation is $\frac{m+6}{10}-\frac{m}{15}=\frac{2}{5}$ .

Formula used:

We take the L.C.M of the denominator.

Use of cross multiplication method.

And then equate the equation both left hand side and right hand side.

Calculation:

Consider the equation

  $\frac{m+6}{10}-\frac{m}{15}=\frac{2}{5}$ .

Now, in the above equation we have $m$ has variable .

Recall that we have to take L.C.M of $\left(10,15\right)$ = $30$ .

Therefore $\frac{3*\left(m+6\right)-2*m}{30}=\frac{2}{5}$ .

Recall that we use cross multiplication method.

Therefore $\frac{3*\left(m+6\right)-2*m}{30}=\frac{2}{5}\Rightarrow \frac{3m+18-2m}{30}=\frac{2}{5}\Rightarrow \frac{m+18}{30}=\frac{2}{5}\Rightarrow 5*\left(m+18\right)=2*30$ .

Recall that we equate the equation both left hand side and right hand side.

Therefore $5*\left(m+18\right)=2*30\Rightarrow 5m+90=60\Rightarrow 5m=-30\Rightarrow m=-6$ .

Therefore the solution of the equations is $m=-6$ .