If 5x-3 - 1x-12x- calculate the value of x-

The correct option is C 97 Given, 5 x+3 = 1 x + 1 2x Taking RHS: 1 x + 1 2x LCM of these is 2x ⇒ 2 2x + 1 2x ⇒ 3 2x No ...

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Standard VIII

Mathematics

Reducing Equations to Simpler Form

If 5x+3 = 1...

Question

If $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$ , calculate the value of $x$ .

\frac{3}{14}

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\frac{1}{3}

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\frac{6}{13}

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\frac{3}{4}

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\frac{9}{7}

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Solution

The correct option is C $\frac{9}{7}$
Given, $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$
Taking RHS:
$\frac{1}{x} + \frac{1}{2 x}$
LCM of these is $2 x$
$\Rightarrow \frac{2}{2 x} + \frac{1}{2 x} \Rightarrow \frac{3}{2 x}$
Now taking LHS:
$\frac{5}{x + 3}$
It is given, LHS $=$ RHS
$\frac{5}{x + 3} = \frac{3}{2 x}$
$\Rightarrow 5 \times 2 x = 3 \times (x + 3) \Rightarrow 10 x = 3 x + 9 \Rightarrow x = \frac{9}{7}$

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Similar questions

Q. If

\frac{x - 3}{6} - \frac{x + 1}{4} = 3

, calculate the value of

x

Expand:
(1) $(a + 2) (a - 1)$
(2) $(m - 4) (m + 6)$
(3) $(p + 8) (p - 3)$
(4) $(13 + x) (13 - x)$
(5) $(3 x + 4 y) (3 x + 5 y)$
(6) $(9 x - 5 t) (9 x + 3 t)$
(7) $(m + \frac{2}{3}) (m - \frac{7}{3})$
(8) $(x + \frac{1}{x}) (x - \frac{1}{x})$
(9) $(\frac{1}{y} + 4) (\frac{1}{y} - 9)$

Solve :

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

$x$	$f (x)$
$1$	$1$
$2$	$3$
$3$	$5$
$4$	$7$
$5$	$9$
$6$	$11$

For the function in the table above, calculate

f (3)

Q. The equation

3^{2 x + 1} - 14 - 3^{x + 1} = \sqrt{1 + 9^{x} + 6 \times 3^{x - 1}}

has

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If 5x+3=1x+12x, calculate the value of x.

The correct option is C 97Given, 5x+3=1x+12xTaking RHS:1x+12xLCM of these is 2x⇒22x+12x⇒32xNow taking LHS:5x+3It is given, LHS = RHS5x+3=32x⇒5×2x=3×(x+3)⇒10x=3x+9⇒x=97

If $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$ , calculate the value of $x$ .