Question

Solve the following equations and check your result:

$\frac{2\mathrm{x}+5}{3}=3\mathrm{x}-10$

Answer 1

Step 1: Finding the solution of a given equation

$$\begin{gathered} \Rightarrow \frac{2\mathrm{x}+5}{3}=3\mathrm{x}-10\left[\mathrm{Given}\right] \\ \Rightarrow \frac{2\mathrm{x}+5}{3}\times 3=(3\mathrm{x}-10)\times 3[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}3] \\ \Rightarrow 2\mathrm{x}+5=3\times 3\mathrm{x}-3\times 10[\mathrm{Distributive}\mathrm{property}] \\ \Rightarrow 2\mathrm{x}+5=9\mathrm{x}-30 \\ \Rightarrow 9\mathrm{x}-30=2\mathrm{x}+5 \\ \Rightarrow 9\mathrm{x}-30+30-2\mathrm{x}=2\mathrm{x}+5+30-2\mathrm{x}[\mathrm{Adding}30\mathrm{and}\mathrm{subtracting}2\mathrm{x}\mathrm{from}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 7\mathrm{x}=35 \\ \Rightarrow \frac{7\mathrm{x}}{7}=\frac{35}{7}[\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}7] \\ \therefore \mathrm{x}=5 \end{gathered}$$

Step 2: Checking the solution of the equation

We will check our results by putting $\mathrm{x}=5$ in the given equation:

So, L.H.S $=\frac{2\mathrm{x}+5}{3}$

$$\begin{gathered} =\frac{2\times 5+5}{3} \\ =\frac{10+5}{3} \\ =\frac{15}{3} \\ =5 \end{gathered}$$

R.H.S$=3\mathrm{x}-10$

$$\begin{gathered} =3\times 5-10 \\ =15-10 \\ =5 \end{gathered}$$

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

Hence, the solution of the given equation is $5$.