Question

solve 9x-7/3x+5=3x-4/x+6​

Answer 1

Step-by-step explanation:

$\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}\\ by\ cross-multiplication\ \\(9x-7)(x+6)=(3x+5)(3x-4)\\9x^2+54x-7x-42=9x^2-12x+15x-20\\9x^2+47x-42=9x^2+3x-20\\47x-3x=-20+42\\44x=22\\ \therefore\ x=\frac{1}{2}$

Answer 2

Answer:

$\large{\underline{\boxed{\sf x = \frac{1}{2} \: \: or \: \: 0.5}}}$

Step-by-step explanation:

$\sf \dfrac{9x - 7}{3x + 5} = \dfrac{3x - 4}{x + 6}$

On cross multiplying, we get :-

$\rightarrow \sf (9x - 7)(x + 6) = (3x + 5)(3x - 4) \\ \\ \rightarrow \sf 9x {}^{2} + 54x - 7x - 42 = 9x {}^{2} - 12x + 15x - 20 \\ \\ \rightarrow \sf 9x {}^{2} + 47x - 42 = 9x {}^{2} + 3x - 20 \\ \\ \rightarrow \sf 9x {}^{2} + 47x - 9x {}^{2} - 3x = 42 - 20 \\ \\ \rightarrow \sf 44x = 22 \\ \\ \rightarrow \sf x = \frac{22}{44} \\ \\ \boxed{ \bf \therefore x = \frac{1}{2} \: \: or \: \: 0.5 }$

Verification:

Substitute the value of x in the given equation:-

$\sf \frac{9x - 7}{3x + 5} = \frac{3x - 4}{x + 6} \\ \\ \sf \frac{9(0.5) - 7}{3(0.5) + 5} = \frac{3(0.5) - 4}{0.5 + 6} \\ \\ \sf \frac{4.5 - 7}{1.5 + 5} = \frac{1.5 - 4}{6.5} \\ \\ \sf \frac{ - 2.5}{6.5} = \frac{ - 2.5}{6.5} \\ \\ \bf \therefore lhs = rhs$

Hence, the answer is ½ or 0.5