Question

Find the solution of the following equations . Also , verify your answer .

$11\left(2x+1\right)-5\left(x+4\right)=9$ .

Answer 1

Given , the linear equation is $11\left(2x+1\right)-5\left(x+4\right)=9----------\left(1\right)$

$\Rightarrow 11\times 2x+11-5x-5\times 4=9$

$\Rightarrow 22x+11-5x-20=9$

$\Rightarrow 17x-9=9$

$\Rightarrow 17x=9+9$

$\Rightarrow 17x=18$

$\Rightarrow x=\frac{18}{17}$

So, the required solution of given equation is $x=\frac{18}{17}$ .

Check :- Putting $x=\frac{18}{17}$ in the equation $\left(1\right)$, we get

LHS $=11\left(2\times \frac{18}{17}+1\right)-5\left(\frac{18}{17}+4\right)$

$=11\left(\frac{36}{17}+1\right)-5\left(\frac{18+68}{17}\right)$

$=11\left(\frac{36+17}{17}\right)-5\left(\frac{86}{17}\right)$

$=11\left(\frac{53}{17}\right)-\left(\frac{430}{17}\right)$

$=\left(\frac{583}{17}\right)-\left(\frac{430}{17}\right)$

$=\left(\frac{583-430}{17}\right)$

$=\left(\frac{153}{17}\right)$

$=9$

Since, LHS $=$ RHS $=$ $9$

Hence, solution $x=\frac{18}{17}$ is satisfy the given equation . So verified .