Question

solve the following questions
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Answer 1

$1) \: 10x + 7 = 3x - 28 \\ 10x - 3x = - 28 - 7 \\ 7x = - 35 \\ x = \frac{ - 35}{7} \\ x = - 5 \\ \\ 2)x + 7 - \frac{8}{3} = \frac{17}{6} - \frac{5x}{2} \\ \\take \: lcm \\ \\ x + \frac{21 - 8}{3} = \frac{17 - 15x}{2} \\ \\ \frac{3x + 21 - 8}{3} = \frac{17 - 15x}{6} \\ \\ \frac{3x + 13}{3} = \frac{17 - 15x}{6} \\ \\ cross \: multiplication \\ \\ 6(3x + 13) = 3(17 - 15x) \\ 18x + 39 = 51 - 45x \\ 18x + 45x = 51 - 39 \\ 63x = 12 \\ x = \frac{12}{63} \\ x = \frac{4}{21} \\ \\ \\ 3) \frac{6x + 1}{3} + 3 = \frac{x - 3}{6} \\ \frac{6x + 1 + 9}{3} = \frac{x - 3}{6} \\ \frac{6x + 10}{3} = \frac{x - 3}{6} \\ 6x + 10 = \frac{x - 3}{2} \\ 2(6x + 10) = x - 3 \\ 12x + 20 = x - 3 \\ 12x - x = - 3 - 20 \\ 11x = - 23 \\ x = \frac{ - 23}{11} \\ \\ \\ 4) \: 5x - 2(2x - 7) = 2(3x - 1) + \frac{7}{3} \\ \\ 10 {x}^{2} - 35x - 4x + 14 = 6x - 2 + \frac{7}{3} \\ \\ 10 {x}^{2} - 39x + 14 = \frac{18x - 6 + 7}{3} \\ \\ 10 {x}^{2} - 39x + 14 = \frac{18x + 1}{3} \\ \\ 30 {x}^{2} - 117x + 42 = 18x + 1 \\ 30 {x}^{2} + 42 - 1 = 18x + 117x \\ 30 {x}^{2} + 41 = 135x \\ 30 {x}^{2} - 135x + 41 = 0$