Question

Solve the following equations and check your result:

$\frac{\mathrm{a}}{8}+\frac{5}{4}=2$

Answer 1

Step 1: Finding the solution of given equation.

$$\begin{gathered} \Rightarrow \frac{\mathrm{a}}{8}+\frac{5}{4}=2\left[\mathrm{Given}\right] \\ \Rightarrow \frac{\mathrm{a}}{8}+\frac{5\times 2}{4\times 2}=2[\mathrm{LCM}\mathrm{of}8\mathrm{and}4\mathrm{is}8,\mathrm{multiply}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{of}\frac{5}{4}\mathrm{by}2] \\ \Rightarrow \frac{\mathrm{a}}{8}+\frac{10}{8}=2 \\ \Rightarrow \frac{\mathrm{a}+10}{8}=2 \\ \Rightarrow \frac{\mathrm{a}+10}{8}\times 8=2\times 8[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}8] \\ \Rightarrow \mathrm{a}+10=16 \\ \Rightarrow \mathrm{a}+10-10=16-10[\mathrm{Subtracting}10\mathrm{from}\mathrm{both}\mathrm{sides}] \\ \therefore \mathrm{a}=6 \end{gathered}$$

Step 2: Checking the solution of the equation

We will check our result by putting $\mathrm{a}=6$ in the given equation;

So, L.H.S $=\frac{\mathrm{a}}{8}+\frac{5}{4}$

$$\begin{gathered} =\frac{6}{8}+\frac{5}{4} \\ =\frac{3}{4}+\frac{5}{4} \\ =\frac{3+5}{4} \\ =\frac{8}{4} \\ =2 \end{gathered}$$

R.H.S$=2$

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

Hence, the solution of the given equation is $2$.