Question

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Answer 1

Respuesta:

Para ver las respuestas mira las fotos <3

23)

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

24)

$2(x + \frac{3}{2} x^{2} - 1) = 3(x ^{2} - 1) \\ 2x + 3x^{2} - 2 =3x^{2} - 3 \\ 2x + 1 = 0 \\ x = - \frac{1}{2}$

25)

$9x - ( \frac{5}{4} + 1)12 = 0 \\ 15x + 12 = 9x \\ 12 = 9x - 15x \\ 12 = - 6x \\ 2 = x$

26)

$(3x + 1)^{2} - 2x = 9x^{2} + 5 \\ 9x^{2} + 6x + 1 = 9x^{2} + 5 \\ 6x = 4 \\ x = \frac{2}{3}$

27)

$8 - 3x + 25x^{2} = (1 - 5x)^{2} \\ 8 - 3x + 25 {x}^{2} = 1 - 10x + 25 {x}^{2} \\ 7 = - 7x \\ 1 = x$

28)

$(x - \frac{3}{2} {)}^{2} = (x + 1)(x - \frac{7}{2} ) - \frac{1}{4} \\ {x}^{2} - 3x + \frac{9}{4} = {x}^{2} - \frac{7}{2} x + x - \frac{7}{2} - \frac{1}{4} \\ - 3x + \frac{9}{4} = - \frac{5}{2} x - \frac{15}{4} \\ \frac{9}{4} + \frac{15}{4} = - \frac{5}{2} x + 3x \\ 6 = 2x \\ 12 = x$

29.

$\frac{2}{3} (9 - 6x) = (3x + 6 {)}^{2} - 9 {x}^{2} - 9 {x}^{2} \\ 6 - 4x = 9 {x}^{2} + 36x + 36 - 9 {x}^{2} \\ - 4x - 36 = 30 \\ - 40x = 30 \\ x = \frac{5}{4}$

30.

$\frac{1}{2} x + \frac{x}{4} + \frac{x}{6} = x - 25 \\ \frac{11}{12} x = x - 25 \\ \frac{11}{12} x - 1x = - 25 \\ - \frac{1}{12} x = - 25 \\ x = \frac{25}{12}$

31.

$\frac{3x - 1}{4} + 1 = \frac{x - 2}{5} + \frac{x - 1}{2} \\ 20( \frac{3x - 1}{4} + 1) = 20( \frac{x - 2}{5} + \frac{x - 1}{2} ) \\ 15x + 15 = 14x - 18 \\( 15 - 14)x = (- 18 - 15) \\ x = - 33$

32)

$\frac{x + 1}{5} - \frac{4x + 2}{3} = \frac{x - 1}{6} \\ 30(\frac{x + 1}{5} - \frac{4x + 2}{3} = 30( \frac{x - 1}{6} ) \\ 6x + 6 - 40x - 20 = 5x - 5 \\ - 34x - 14 = 5x - 5 \\ - 34x - 5x = - 5 + 14 \\ - 39x = 9 \\ x = - \frac{3}{13}$

33)

$\frac{x + 3}{6} = \frac{2x - 4}{3} \\ 3( \frac{x + 3}{6}) = 3( \frac{2x - 4}{3}) \\ 3x + 9 = - 12 + 24 \\ 3x + 12x = 24 - 9 \\ 15x = 15 \\ x = 1$

34)

$\frac{x}{2} - \frac{2x - 3}{5} = \frac{x + 3}{2} + \frac{x}{5} \\ 10( \frac{x}{2} - \frac{2x - 3}{5}) = 5(\frac{x + 3}{2} + \frac{x}{5} ) \\ 5x - 2(2x - 3) = 5(x + 3) + 2x \\ 5x - 4x + 6 = 5x + 15 + 2x \\ - 4x + 6 = 15 + 2x \\ - 4x - 2x = 15 - 6 \\ - 6x = 9 \\ x = - \frac{3}{2}$

35)

$1 - \frac{2x + 3}{5} - 1.5 = \frac{3}{2} x - x \\ - \frac{2x + 3}{5} - \frac{1}{2} = \frac{3}{2} x - x \\ 10(- \frac{2x + 3}{5} - \frac{1}{2} )=10( \frac{3}{2} x - x ) \\ - 5 - 2(2x + 3) = 15x - 10x \\ - 5 - 4x - 6 = 5x \\ - 11 - 4x = 5x \\ - 4x - 5x = 11 \\ - 9x = 11 \\ x = - \frac{11}{9}$

36)$\frac{(x - 1)^{2} }{6} - \frac{0.5 {x}^{2} - 1 }{3} = 0 \\ \frac{ {x}^{2} - 2x + 1}{6} - \frac{ \frac{1}{2}x^{2} - 1 }{3} = 0 \\ \frac{ {x}^{2} - 2x + 1 }{6} - \frac{ \frac{ {x}^{2} - 2 }{2} }{3} = 0 \\ \frac{ {x}^{2} - 2x + 1 }{6} - \frac{ {x}^{2} - 2 }{6} = 0 \\ {x}^{2} - 2x + 1 - ( {x}^{2} - 2) = 0 \\ {x}^{2} - 2x + 1 - {x}^{2} + 2 = 0 \\ - 2x + 3 = 0 \\ - 2x = - 3 \\ x = \frac{3}{2}$

37)

$\frac{5 - 2x}{3} - (1 - \frac{3 {x}^{2} - 1 }{2} ) + 5 = 0 \\ \frac{5 - 2x}{3} - 1 + \frac{3x - 1}{2} + 5 = 0 \\ 6(\frac{5 - 2x}{3} - 1 + \frac{3x - 1}{2} + 5) =6( 0 ) \\ \frac{5 - 2x}{3} + 4 + \frac{3x - 1}{2} = 0 \\ 2(5 - 2x) + 24 + 3(3x - 1) = 0 \\ 10 - 4x + 24 + 9x - 3 = 0 \\ 31 + 5x = 0 \\ 5x = - 31 \\ x = - \frac{ 31}{5}$

38)

$\frac{3 + 2x}{5} - (2 - \frac{3 - x}{3} ) = x \\ \frac{3 + 2x}{5} - 2 + \frac{3 - x}{3} = x \\ 15(\frac{3 + 2x}{5} - 2 + \frac{3 - x}{3} ) = 15x \\ 3(3 + 2x) - 30 + 5(3 - x) = 15x \\ 9 + 6x - 30 + 15 - 5x = 15x \\ - 6x + x = 15x \\ \times - 15x = 6 \\ x - 15x = 6 \\ - 14x = 6 \\ x = - \frac{6}{14} \\ x = - \frac{3}{7}$

39)

$2 {x}^{2} - 50 = 0 \\ 2x^{2} = 50 \div 2\\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5$

40)

${x}^{2} + 49 = 0 \\ falso$

41)

$2x^{2} = 3 {x}^{2} + 36 \\ 2 {x}^{2} - 3 {x}^{2} = 36 \\ - {x}^{2} = 36 \\ x ^{2} = 36 \\ falso$