Question

Solve the following equations and check your result:

$\frac{4\mathrm{m}+2}{6\mathrm{m}+10}=\frac{1}{2}$

Answer 1

Step 1: Finding the solution of a given equation

$$\begin{gathered} \Rightarrow \frac{4\mathrm{m}+2}{6\mathrm{m}+10}=\frac{1}{2}\left[\mathrm{Given}\right] \\ \Rightarrow \frac{4\mathrm{m}+2}{(6\mathrm{m}+10)}\times (6\mathrm{m}+10)=\frac{1}{2}\times (6\mathrm{m}+10)[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}(6\mathrm{m}+10\left)\right] \\ \Rightarrow 4\mathrm{m}+2=\frac{1}{2}\times 6\mathrm{m}+\frac{1}{2}\times 10[\mathrm{Distributive}\mathrm{property}] \\ \Rightarrow 4\mathrm{m}+2=3\mathrm{m}+5 \\ \Rightarrow 4\mathrm{m}+2-3\mathrm{m}-2=3\mathrm{m}+5-3\mathrm{m}-2[\mathrm{Subtracting}3\mathrm{m}\mathrm{and}2\mathrm{from}\mathrm{both}\mathrm{sides}] \\ \therefore \mathrm{m}=3 \end{gathered}$$

Step 2: Checking the solution of the equation

We will check our result by putting $\mathrm{m}=3$ in the given equation;

So, L.H.S $=\frac{4\mathrm{m}+2}{6\mathrm{m}+10}$

$$\begin{gathered} =\frac{4\times 3+2}{6\times 3+10} \\ =\frac{12+2}{18+10} \\ =\frac{14}{28} \\ =\frac{1}{2} \end{gathered}$$

R.H.S$=\frac{1}{2}$

$\therefore \mathrm{L}.\mathrm{H}.\mathrm{S}=\mathrm{R}.\mathrm{H}.\mathrm{S}$

Hence, the solution of the given equation is $3$.