Question

Solve the equation
$\frac{4x - 3}{2x + 3} = \frac{5}{7}$
​

Answer 1

Hope it's Helpful for you.....☺☺

Answer 2

$\mathfrak{\underline{\underline{\large{Solution:-}}}}$

Multiplying both sides of the above equation by (2x + 3 ), we get,

$\frac{4x - 3}{2x + 3} \times (2x + 3) = \frac{5}{7} \times (2x + 3)$

$= > 4x - 3 = \frac{5}{7} (2x + 3)$

$\sf{\red{The \:denominator \:of\: R.H.S \:is \:7,}}$

$4x - 3 = \frac{5}{7} (2x + 3)$

$4x - 3 = \frac{10}{7} x - \frac{15}{7}$

$= > 4x - \frac{10}{7} x = \frac{15}{7} + 3$

$= > \frac{28x - 10x}{7} = \frac{15 + 21}{7}$

$= > \frac{18}{7} x = \frac{36}{7}$

$= > x = \frac{36}{7} \times \frac{7}{18} = 2$

$\mathfrak{\underline{\underline{\large{Verification:-}}}}$

$\sf{\orange{Put\: x = 2 in\: L.H.S \:of\: the \:equation}}$

L.H.S.

$\frac{4x - 3}{2x + 3} = \frac{4 \times 2 - 3}{2 \times 2 + 3} = \frac{8 - 3}{4 + 3} = \frac{5}{7}$

$\sf{\purlle{Hence,\: x = 2 is\: the\: solution.}}$

$\bold{\underline{\underline{\large{Note:-}}}}$

$\sf{\green{The \:equation \frac{4x - 3}{2x + 3} = \frac{5}{7} can \:be\: written\: as: }}$

$\frac{4x - 3}{2x + 3} \times (2x + 3) \times 7 = \frac{5}{7} \times (2x + 3) \times 7$

or

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

Now, the given equation is reduced to the form of linear equation in one variable.