[tex]5) \frac{2a - 3b}{3a + b} = \frac{2}{5} [/tex]
[tex]5(2a - 3b) = 2(3a + b)[/tex]
[tex]10a - 15b = 6a + 2b[/tex]
[tex]10a - 6a = 2b + 15b[/tex]
[tex]4a = 17b \: | \div b[/tex]
[tex] \frac{4a}{b} = 17[/tex]
[tex]4 \times \frac{a}{b} = 17 \: | \div 4[/tex]
[tex] \frac{a}{b} = \frac{17}{4} [/tex]
[tex]6)a) \frac{x}{6} = \frac{3}{2} [/tex]
[tex]x = \frac{6 \times 3}{2} = 3 \times 3 = 9[/tex]
[tex]b) \frac{2x - 1}{5} = 3[/tex]
[tex]2x - 1 = 5 \times 3[/tex]
[tex]2x - 1 = 15[/tex]
[tex]2x = 15 + 1[/tex]
[tex]2x = 16 [/tex]
[tex]x = \frac{16}{2} [/tex]
[tex]x = 8[/tex]
[tex]c) \frac{x + 2}{x + 4} = \frac{4}{5} [/tex]
[tex]5(x + 2) = 4(x + 4)[/tex]
[tex]5x + 10 = 4x + 16[/tex]
[tex]5x - 4x = 16 - 10[/tex]
[tex]x = 6[/tex]
[tex]d) \frac{65}{ {x}^{3} } = \frac{ {x}^{3} + 1}{64} [/tex]
[tex] {x}^{3} ( {x}^{3} + 1) = 64 \times 65[/tex]
[tex] {x}^{3} ( {x}^{3} + 1) = 64(64 + 1)[/tex]
[tex] = > {x}^{3} = 64 = > x = 4[/tex]
[tex]e) \frac{ {2}^{2002} - {2}^{2001} - {2}^{2000} }{ {4}^{1000} } = \frac{x}{5} [/tex]
[tex] \frac{ {2}^{2000} ( {2}^{2} - 2 - 1)}{( {{2}^{2} )}^{1000} } = \frac{x}{5} [/tex]
[tex] \frac{ {2}^{2000} (4 - 2 - 1)}{ {2}^{2 \times 1000} } = \frac{x}{5} [/tex]
[tex] \frac{ {2}^{2000} \times 1}{ {2}^{2000} } = \frac{x}{5} [/tex]
[tex]1 = \frac{x}{5} [/tex]
[tex]x = 5 \times 1[/tex]
[tex]x = 5[/tex]
