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Performing Mathematical Operations on Equation

Solve:x-52-x-...

Question

Solve:
$\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2}$

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Solution

$\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2} \Rightarrow 10 (\frac{x - 5}{2}) - 10 (\frac{x - 3}{5}) = 10 (\frac{1}{2}) (multiplying throughout by 10, which is the L . C . M . of 2, 2 and 5) \Rightarrow 5 (x - 5) - 2 (x - 3) = 5 \Rightarrow 5 x - 25 - 2 x + 6 = 5 \Rightarrow 5 x - 2 x - 25 + 6 = 5 \Rightarrow 3 x - 19 = 5 \Rightarrow 3 x = 5 + 19 \Rightarrow 3 x = 24 \Rightarrow x = \frac{24}{3} = 8 ∴ x = 8$

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Similar questions

$x$	$3$	$4$	$5$	$6$	$7$
$f$	$12$	$35$	$52$	$41$	$18$

\frac{6}{5} x^{2} - \frac{4}{5} x^{3} + \frac{5}{6} + \frac{3}{2} x from \frac{x^{3}}{3} - \frac{5}{2} x^{2} + \frac{3}{5} x + \frac{1}{4}

\frac{5 a^{2}}{2} + \frac{3 a^{3}}{2} + \frac{a}{3} - \frac{6}{5} from \frac{1}{3} a^{3} - \frac{3}{4} a^{2} - \frac{5}{2}

\frac{7}{4} x^{3} + \frac{3}{5} x^{2} + \frac{1}{2} x + \frac{9}{2} from \frac{7}{2} - \frac{x}{3} - \frac{x^{2}}{5}

\frac{y^{3}}{3} + \frac{7}{3} y^{2} + \frac{1}{2} y + \frac{1}{2} from \frac{1}{3} - \frac{5}{3} y^{2}

\frac{2}{3} a c - \frac{5}{7} a b + \frac{2}{3} b c from \frac{3}{2} a b - \frac{7}{4} a c - \frac{5}{6} b c

Solve :

$\frac{x - 5}{2} - \frac{x - 3}{5} = \frac{1}{2}$

Now can you reduce each of these products to a single power?

(i) 5² × 5² × 5⁶

(ii) 7⁴ × 7⁹ × 7²

(iii) 4² × 4² × 4²

(iv) 3⁵ × 3⁵ × 3⁵ × 3⁵

\frac{3}{x + y} + \frac{2}{x - y} = 2 and \frac{9}{x + y} - \frac{4}{x - y} = 1

x = \frac{1}{2}, y = \frac{3}{2}

x = \frac{5}{2}, y = \frac{1}{2}

x = \frac{3}{2}, y = \frac{1}{2}

x = \frac{1}{2}, y = \frac{5}{2}

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