Question

Solve each of the following equations and also check your results in each case:

(iv) $x-2x+2-\frac{16}{3}x+5=3-\frac{7}{2}x$

Answer 1

Given: $x-2x+2-\frac{16}{3}x+5=3-\frac{7}{2}x$

$\Rightarrow x-2x-\frac{16x}{3}+\frac{7x}{2}=3-2-5$

$\Rightarrow \frac{6x-12x-32x+21x}{6}=-4$

$\Rightarrow -\frac{17x}{6}=-4$

$\Rightarrow -17x=-4\times 6$

$\Rightarrow -17x=-24$

$\Rightarrow x=\frac{-24}{-17}$

$\Rightarrow x=\frac{24}{17}$

To check: $x-2x+2-\frac{16}{3}x+5=3-\frac{7}{2}x$

for $x=\frac{24}{17}$

$L.H.S=x-2x+2-\frac{16}{3}x+5$

$=\frac{24}{17}-2\left(\frac{24}{17}\right)+2-\left(\frac{16}{3}\right)\left(\frac{24}{17}\right)+5$

$=\frac{24}{17}-\frac{48}{17}+2-\frac{128}{17}+5$

$=\frac{24-48+34-128+85}{17}$

$=-\frac{33}{17}$

$R.H.S=3-\frac{7}{2}x$

$=3-\left(\frac{7}{2}\right)\left(\frac{24}{17}\right)$

$=3-\frac{168}{34}$

$=\frac{102-168}{34}$

$=-\frac{66}{34}$

$=-\frac{33}{17}$

$\therefore L.H.S=R.H.S$

Hence, the given equation is verified for $x=\frac{24}{17}$.