Question

Solve the following equations and check your result:

$\frac{\mathrm{b}+5}{11}+\frac{3\mathrm{b}-8}{2}=6$

Answer 1

Step 1: Finding the solution of a given equation

$$\begin{gathered} \Rightarrow \frac{\mathrm{b}+5}{11}+\frac{3\mathrm{b}-8}{2}=6\left[\mathrm{Given}\right] \\ \Rightarrow \frac{(\mathrm{b}+5)\times 2+(3\mathrm{b}-8)\times 11}{11\times 2}=6 \\ \Rightarrow \frac{2\times \mathrm{b}+5\times 2+3\mathrm{b}\times 11-8\times 11}{22}=6[\mathrm{Distributive}\mathrm{property}] \\ \Rightarrow \frac{2\mathrm{b}+10+33\mathrm{b}-88}{22}\times 22=6\times 22[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}22] \\ \Rightarrow 35\mathrm{b}-78=132 \\ \Rightarrow 35\mathrm{b}-78+78=132+78[\mathrm{Adding}78\mathrm{to}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 35\mathrm{b}=210 \\ \Rightarrow \frac{35\mathrm{b}}{35}=\frac{210}{35}[\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}35] \\ \therefore \mathrm{b}=6 \end{gathered}$$

Step 2: Checking the solution of the equation

we will check our results by putting $\mathrm{b}=6$ in the given equation:

So, L.H.S $=\frac{\mathrm{b}+5}{11}+\frac{3\mathrm{b}-8}{2}$

$$\begin{gathered} =\frac{6+5}{11}+\frac{3\times 6-8}{2} \\ =\frac{11}{11}+\frac{18-8}{2} \\ =1+\frac{10}{2} \\ =1+5 \\ =6 \end{gathered}$$

R.H.S$=6$

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

Hence, the solution of the given equation is $6$.