Question

Solve the following equation and verify your answer:

$\left(iv\right)$ $\frac{3x+5}{2x+7}=4$

Answer 1

Given: $\frac{3x+5}{2x+7}=4$

$(3x+5)=4(2x+7)$

$3x+5=8x+28$

$3x-8x=28-5$

$-5x=23$

$x=-\frac{23}{5}$

To check: $\frac{3x+5}{2x+7}=4$ for $x=-\frac{23}{5}$

$\text{L.H.S}=\frac{3x+5}{2x+7}$

$=\left[\frac{3(-\frac{23}{5})+5}{2(-\frac{23}{5})+7}\right]$

$=\frac{(-\frac{69}{5}+5)}{(-\frac{46}{5}+7)}$

$=\frac{\left(\frac{-69+25}{5}\right)}{\left(\frac{-46+35}{5}\right)}$

$=\frac{-\frac{44}{5}}{-\frac{11}{5}}$

$=\frac{-44}{5}\times \frac{5}{-11}$

$=\frac{44}{11}$

$=4=\text{R.H.S}$

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

Hence, the given equation is verified for $x=-\frac{23}{5}.$