Question

responde las siguientes ecuaciones​

Answer 1

Respuesta:

$a)3x + 5 = 5x - 13 \\ 5 + 13 = 5x - 3x \\ 18 = 2x \\ 9 = x$

$b)5(7 - x) = 31 - x \\ 35 - 5x = 31 - x \\ 35 - 31 = - x + 5x \\ 4 = 4x \\ 1 = x$

$c)4(2 - 3x) = - 2x - 27 \\ 8 - 12x = - 2x - 27 \\ 8 + 27 = - 2x + 12x \\ 35 = 10x \\ \frac{35}{10} = x \\ \frac{7}{2} = x$

$d)6x - 8 = 4( - 2x + 5) \\ 6x - 8 = - 8x + 20 \\ 6x + 8x = 20 + 8 \\ 14x = 28 \\ x = 2$

$f)3(4x + 7) = 4x - 25 \\ 12x + 21 = 4x - 25 \\ 12x - 4x = - 25 - 21 \\ 8x = - 46 \\x = \frac{ - 46}{8} \\ x = - \frac{23}{4}$

$g)7x + 15 = 3(3x - 7) \\ 7x + 15 = 9x - 21 \\ 15 + 21 = 9x - 7x \\ 36 = 2x \\ \frac{36}{2} = x \\ 18 = x$

$h) \frac{4x + 1}{3} = \frac{12x - 3}{7} \\ 21( \frac{4x + 1}{3} ) = 21( \frac{12x - 3}{7} ) \\ 7(4x + 1) = 3(12x - 3) \\ 28x + 7 = 36x - 9 \\ 7 + 9 = 36x - 28x \\ 16 = 8x \\ 2 = x$

$i) \frac{2x - 5}{12} = \frac{ - x}{4} - \frac{5}{3} \\ 12( \frac{2x - 5}{12} ) = 12( \frac{ - x}{4} - \frac{5}{3} ) \\ 2x - 5 = - 3x - 20 \\ 2x + 3x = - 20 + 5 \\ 5x = - 15 \\ x = - 3$

$j) \frac{x}{5} + \frac{x}{3} - 1 = \frac{x}{2} \\ 30( \frac{x}{5} + \frac{x}{3} - 1 ) = 30 \times \frac{x}{2} \\ 6x + 10x - 30 = 15x \\ 16x - 30 = 15x \\ 16x - 15x = 30 \\ x = 30$

$k) \frac{2x + 4}{3} = \frac{x}{6} - 3 \\ 6( \frac{2x + 4}{3} ) = 6( \frac{x}{6} - 3) \\ 2(2x + 4) = x - 18 \\ 4x + 8 = x - 18 \\ 4x - x = - 18 - 8 \\ 3x = - 26 \\ x = - \frac{26}{3}$

$l) \frac{x + 11}{2} - \frac{2x + 3}{5} = 5 \\ 10( \frac{x + 11}{2} - \frac{2x + 3}{5} ) = 5 \times 10 \\ 5(x + 11) - 2(2x + 3) = 50 \\ 5x + 55 - 4x - 6 = 50 \\ x + 49 = 50 \\ x = 50 - 49 \\ x = 1$

$m) \frac{5x + 1}{6} + \frac{2x + 1}{3} = 2 \\ 6( \frac{5x + 1}{6} + \frac{2x + 1}{3} ) = 2 \times 6 \\ 5x + 1 + 2(2x + 1) = 12 \\ 5x + 1 + 4x + 2 = 12 \\ 9x + 3 = 12 \\ 9x = 12 - 3 \\ 9x = 9 \\ x = 1$

$n) \frac{x + 1}{5} = - 10 + \frac{2x + 1}{3} \\ 15( \frac{x + 1}{5} ) = 15( - 10 + \frac{2x + 1}{3} ) \\ 3(x + 1) = - 150 + 5(2x + 1) \\ 3x + 3 = - 150 + 10x + 5 \\ 3x + 3 = - 145 + 10x \\3 + 145 = 10x - 3x \\ 148 = 7x \\ \frac{148}{7} = x$

$o)x - \frac{x}{5} = 30 \\ 5(x - \frac{x}{5} ) = 5 \times 30 \\ 5x - x = 150 \\ 4x = 150 \\ x = \frac{150}{4} = \frac{75}{2}$

$q) \frac{4x}{15} - \frac{6x + 28}{5} = 0 \\ 15( \frac{4x}{15} - \frac{6x + 28}{5} ) = 0 \times 15 \\ 4x - 3(6x + 28) = 0 \\ 4x - 18x - 84 = 0 \\ - 14x - 84 = 0 \\ - 84 = 14x \\ - 6 = x$

$r) \frac{2x}{3} = \frac{5x}{12} - 2 \\ 12( \frac{2x}{3} ) = 12( \frac{5x}{12} - 2) \\ 8x = 5x - 24 \\ 24 = 5x - 8x \\ 24 = - 3x \\ - 8 = x$

$s)3x - \frac{2x}{5} = \frac{3x}{10} + 14 \\ 10(3x - \frac{2x}{5} ) = 10( \frac{3x}{10} + 14) \\ 30x - 4x = 3x + 140 \\ 26x = 3x + 140 \\ 26x - 3x = 140 \\ 23x = 140 \\ x = \frac{140}{23}$

$t) \frac{4x - 3}{5} - \frac{4x}{3} = \frac{2(x - 13)}{15} \\ \frac{4x - 3}{5} - \frac{4x}{3} = \frac{2x - 26}{15} \\ 15( \frac{4x - 3}{5} - \frac{4x}{3} ) = 15( \frac{2x - 26}{15} ) \\ 3(4x - 3) - 20x = 2x - 26 \\ 12x - 9 - 20x = 2x - 26 \\ - 8x - 9 = 2x - 26 \\ - 9 + 26 = 2x + 8x \\ 17 = 10x \\ \frac{17}{10} = x$

$u) \frac{3x + 5}{2} - \frac{4x - 5}{3} = \frac{7x + 1}{6} - 5 \\ 6( \frac{3x + 5}{2} - \frac{4x - 5}{3} ) = 6( \frac{7x + 1}{6} - 5) \\ 3(3x + 5) - 2(4x - 5) = 7x + 1 - 30 \\ 9x + 15 + 8x + 10 = 7x + 1 - 30 \\ 17x + 25 = 7x - 29 \\ 17x - 7x = - 29 - 25 \\ 10x = - 54 \\ x = - \frac{54}{10} = - \frac{27}{5}$

$v) \frac{9x - 1}{13} - \frac{5x - 8}{4} = x + 6 \\ 52( \frac{9x - 1}{13} - \frac{5x - 8}{4} ) = 52(x + 6) \\ 4(9x - 1) -13 (5x - 8) = 52x + 312 \\ 36x - 4 - 65x + 104 = 52x + 312 \\ - 29x + 100 = 52x + 312 \\ 100 - 312 = 52x + 29x \\ - 212 = 81x \\ - \frac{212}{81} = x$

$x) \frac{4(3x + 6)}{5} + 3 = \frac{2(2x + 5)}{3} - 3x \\ \frac{12x + 24}{5} + 3 = \frac{4x + 10}{3} - 3x \\ 15( \frac{12x - 24}{5} + 3 ) = 15( \frac{4x + 10}{3} - 3x) \\ 3(12x - 24) + 45 = 5(4x + 10) - 45x \\ 36x - 72 + 45 = 20x + 50 - 45x \\ 36x - 27 = - 25x + 50 \\ 36x + 25x = 50 + 27 \\ 51x = 77 \\ x = \frac{77}{51}$

$y)2x - 6 - \frac{2(2x + 8)}{3} = 4x - 1 \\ 2x - 6 - \frac{4x + 16}{3} = 4x - 1 \\ 3(2x - 6 - \frac{4x + 16}{3} ) = 3(4x - 1) \\ 6x - 18 - (4x + 16) = 12x - 3 \\ 6x - 18 - 4x - 16 = 12x - 3 \\ 2x - 34 = 12x - 3 \\ - 34 + 3 = 12x - 2x \\ - 31 = 10x \\ - \frac{31}{10} = x$

$z) \frac{7x - 6}{3} - (x + 2) = 4x + 2 \\ \frac{7x - 6}{3} - x - 2 = 4x + 2 \\ 3( \frac{7x - 6}{3} - x - 2 ) = 3(4x + 2) \\ 7x - 6 - 3x - 6 = 12x + 6 \\ 4x - 12 = 12x + 6 \\ - 12 - 6 = 12x - 4x \\ - 18 = 8x \\ \frac{ - 18}{8} = x \\ - \frac{9}{4} = x$