Solve - 9x-7-3x-5-3x-4-x-6

9x 7/3x+5=3x 4/x+6 By cross multiplication, (9x 7)(x+6)=(3x 4)(3x+5) 9x^2+54x 7x 42=9x^2+15x 12x 20 ⇒ 9x^2+54x 7x 9x^2 15x+12x= 20+42 ⇒ 66x 22x=22⇒ 44x=22 ⇒ x= ...

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Byju's Answer

Standard VIII

Mathematics

Equations Reducible to the Linear Form

Solve : 9x-7/...

Question

Solve :

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

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Solution

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

By cross multiplication,

$(9 x - 7) (x + 6) = (3 x - 4) (3 x + 5) 9 x^{2} + 54 x - 7 x - 42 = 9 x^{2} + 15 x - 12 x - 20 \Rightarrow 9 x^{2} + 54 x - 7 x - 9 x^{2} - 15 x + 12 x = - 20 + 42 \Rightarrow 66 x - 22 x = 22 \Rightarrow 44 x = 22 \Rightarrow x = \frac{22}{44} = \frac{1}{2} Hence x = \frac{1}{2} A n s .$

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Similar questions

Q. Solve :

\int \frac{x^{6} - 2 x^{4} + 3 x^{3} - 9 x^{2} + 4}{x^{5} - 5 x^{3} + 4 x} d x

Q. Solve:

\frac{9 x - 7}{3 x + 5} = \frac{3 x - 4}{x + 6}

Q. Prove that :

\frac{(sin 7 x + sin 5 x) + (sin 9 x + sin 3 x)}{(cos 7 x + cos 5 x) + (cos 9 x + cos 3 x)} = tan 6 x

Solve:-

(i) $5 (3 x - 4) - 8 (6 x - 7) = 9 x - 8$

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

(iii) $\frac{2 z}{3} - 5 = \frac{3 z}{4} - 1$

(iv) $\frac{4 x}{7} - 12 = 7$

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

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Solve : 9x−73x+5=3x−4x+6

9x−73x+5=3x−4x+6 By cross multiplication, (9x−7)(x+6)=(3x−4)(3x+5)9x2+54x−7x−42=9x2+15x−12x−20⇒ 9x2+54x−7x−9x2−15x+12x=−20+42⇒ 66x−22x=22⇒ 44x=22⇒ x=2244=12Hence x=12 Ans.

Solve :

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