Solve the following equations:
(1) $x - 4 = 3$ ,
(2) $2 a + 4 = 0,$
(3) $17 p - 2 = 49$
(4) $2 m + 7 = 9$
(5) $5 (x - 3) = 3 (x + 2)$
(6) $13 x - 5 = \frac{3}{2}$

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Solution

$1)$ $x - 4 = 3 x = 7$

$2)$ $2 a + 4 = 0 a = - 2$

$1)$ $17 p - 2 = 49 17 p = 51 p = 3$

$2)$ $2 m + 7 = 9 2 m = 2 m = 1$

$3)$ $5 (x - 3) = 3 (x + 2) 5 x - 15 = 3 x + 6 2 x = 21 x = \frac{21}{2} = 10 \frac{1}{2}$

$6)$ $13 x - 5 = \frac{3}{2} 13 x = \frac{3}{2} + 5 13 x = \frac{13}{2} x = \frac{1}{2}$

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