Solve- 2 x - 2-2x - 3 - 9 2x - 3-x - 2 - 3-

The correct option is C None of these 2 ( x+22x 3 ) 9 ( 2x 3x+2 )=3 ⇒ 2(x+2)^2 9(2x 3)^2=3(2x 3)(x+2) ⇒ 2(x^2+4x+4) 9(4x^2 12x+9)=3(2x^2 3x+4x 6) ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Equation

Solve: 2 x ...

Question

Solve: $2 (\frac{x + 2}{2 x - 3}) - 9 (\frac{2 x - 3}{x + 2}) = 3$ .

x = \frac{12}{5}, x = \frac{1}{8}

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x = \frac{18}{5}, x = \frac{7}{12}

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x = \frac{16}{9}, x = \frac{5}{8}

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None of these

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Solution

The correct option is C None of these
$2 (\frac{x + 2}{2 x - 3}) - 9 (\frac{2 x - 3}{x + 2}) = 3$
$\Rightarrow 2 (x + 2)^{2} - 9 (2 x - 3)^{2} = 3 (2 x - 3) (x + 2)$
$\Rightarrow 2 (x^{2} + 4 x + 4) - 9 (4 x^{2} - 12 x + 9) = 3 (2 x^{2} - 3 x + 4 x - 6)$
$\Rightarrow 2 x^{2} + 8 x + 8 - 36 x^{2} + 108 x - 81 = 6 x^{2} - 9 x + 12 x - 18$
$\Rightarrow 2 x^{2} - 36 x^{2} - 6 x^{2} + 8 x + 108 x + 9 x - 12 x - 81 + 8 - 18$
$\Rightarrow - 40 x^{2} + 113 x + 55 = 0$
$\Rightarrow 40 x^{2} - 113 x + 55 = 0$
$\Rightarrow 40 x^{2} - 88 x - 25 x + 55 = 0$
$\Rightarrow 8 x (5 x - 11) - 5 (5 x - 11) = 0$
$\Rightarrow (5 x - 11) (8 x - 11) = 0$
$∴ 5 x - 11 = 0$
$\Rightarrow x = \frac{11}{5}$
$∴ 8 x - 11 = 0$
$\Rightarrow x = \frac{11}{8}$

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Similar questions

Q. Solve the following equations.
(1) 17p − 2 = 49
(2) 2m + 7 = 9
(3) 3x + 12 = 2x − 4
(4) 5(x − 3) = 3(x + 2)

(5)

\frac{9 x}{8}

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(6)

\frac{y}{7}

\frac{y - 4}{3}

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(7) 13x − 5 =

\frac{3}{2}

(8) 3(y + 8) = 10(y − 4) + 8

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Q. Solve:

x + 6 - 3 x - 5 - 2 (x - 5) = 2 x - 9 - 2 x + 5 - 3 (x + 1)

Solve the following:

(i) x + 3 = 11; (ii) y − 9 = 21; (iii) 10 = z + 3; (iv) ; (v) 10x = 30; (vi) ;

(vii) ; (viii) ; (ix) 8x − 8 = 48; (x) ; (xi) ; (xii) ;

(xiii) 3 (x + 6) = 24; (xiv) ; (xv) 3(x + 2) − 2(x − 1) = 7.

Q. Solve the following equation:

8 (x - 3) - (6 - 2 x) = 2 (x + 2) - 5 (5 - x)

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: 2(x+22x−3)−9(2x−3x+2)=3.

Solve: $2 (\frac{x + 2}{2 x - 3}) - 9 (\frac{2 x - 3}{x + 2}) = 3$ .