Question

Ma puteti ajuta la exercitile 5 si 6 Varogggg mult!!

Answer 1

$5) \frac{2a - 3b}{3a + b} = \frac{2}{5}$

$5(2a - 3b) = 2(3a + b)$

$10a - 15b = 6a + 2b$

$10a - 6a = 2b + 15b$

$4a = 17b \: | \div b$

$\frac{4a}{b} = 17$

$4 \times \frac{a}{b} = 17 \: | \div 4$

$\frac{a}{b} = \frac{17}{4}$

$6)a) \frac{x}{6} = \frac{3}{2}$

$x = \frac{6 \times 3}{2} = 3 \times 3 = 9$

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

$2x - 1 = 5 \times 3$

$2x - 1 = 15$

$2x = 15 + 1$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

$c) \frac{x + 2}{x + 4} = \frac{4}{5}$

$5(x + 2) = 4(x + 4)$

$5x + 10 = 4x + 16$

$5x - 4x = 16 - 10$

$x = 6$

$d) \frac{65}{ {x}^{3} } = \frac{ {x}^{3} + 1}{64}$

${x}^{3} ( {x}^{3} + 1) = 64 \times 65$

${x}^{3} ( {x}^{3} + 1) = 64(64 + 1)$

$= > {x}^{3} = 64 = > x = 4$

$e) \frac{ {2}^{2002} - {2}^{2001} - {2}^{2000} }{ {4}^{1000} } = \frac{x}{5}$

$\frac{ {2}^{2000} ( {2}^{2} - 2 - 1)}{( {{2}^{2} )}^{1000} } = \frac{x}{5}$

$\frac{ {2}^{2000} (4 - 2 - 1)}{ {2}^{2 \times 1000} } = \frac{x}{5}$

$\frac{ {2}^{2000} \times 1}{ {2}^{2000} } = \frac{x}{5}$

$1 = \frac{x}{5}$

$x = 5 \times 1$

$x = 5$