Question

10 Rezolvați ecuațiile în mulţimea numerelor reale: a) 5(3x - 2) - 6(8x - 13) - 13x = 16(8 - 3x) - 62; b) 2(3x - 4) + 5(6x - 7) - 7x = 16(x +15) - 10; c) 3(6x - 5) - 2(4x + 13) + 5 = 5(4 - x) - 26; d) 7x + 4 + 2(x - 5) = 8x + 1; e) 2(3x + 4) - 5(2x - 3) + 7 = 7(x - 1) + 4; f) 2(x + 3) - 5(2x + 1) = 12x - 19; g) 3(2x + 3) + 2(3x + 2) = 9x + 4; h) 5(x - 2) - 2x - (6 + 7x) = 3(-x-1); i) 4(x + 6) -6(x - 1) = 3x - 5; j) 6(x + 2) - 2(2x + 3) + 4x = 36; k) 3(x+2) -(4x + 1) = 2(4-x); 1) 5(x - 2) + 4x - 3 = 6x +11; m) 5(x + 2) - (7 + 5x) = 3x; n) 5(x - 1) + 3x - 4 = 3x + 11; o) 7(x + 3) - 3x = 5 + 6(x + 5) -
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Answer 1

Explicație pas cu pas:

a) 5(3x - 2) - 6(8x - 13) - 13x = 16(8 - 3x) - 62

$5(3x - 2) - 6(8x - 13) - 13x = 16(8 - 3x) - 62 \\ 15x - 10 - 48x + 78 - 13x = 128 - 48x - 62 \\ - 46x + 48x = 66 - 68 \\ 2x = - 2 \\ x = - 1$

b) 2(3x - 4) + 5(6x - 7) - 7x = 16(x +15) - 10

$2(3x - 4) + 5(6x - 7) - 7x = 16(x +15) - 10 \\ 6x - 8 + 30x - 35 - 7x = 16x + 240 - 10 \\ 29x - 16x = 230 + 43 \\ 13x = 273 \\ x = 21$

c) 3(6x - 5) - 2(4x + 13) + 5 = 5(4 - x) - 26

$3(6x - 5) - 2(4x + 13) + 5 = 5(4 - x) - 26 \\ 18x - 15 - 8x - 26 + 5 = 20 - 5x - 26 \\ 10x + 5x = - 6 + 36 \\ 15x = 30 \\ x = 2$

d) 7x + 4 + 2(x - 5) = 8x + 1

$7x + 4 + 2(x - 5) = 8x + 1 \\ 7x + 4 + 2x - 10 = 8x + 1 \\ 9x - 8x = 1 + 6 \\ x = 7$

e) 2(3x + 4) - 5(2x - 3) + 7 = 7(x - 1) + 4

$2(3x + 4) - 5(2x - 3) + 7 = 7(x - 1) + 4 \\ 6x + 8 - 10x + 15 + 7 = 7x - 7 + 4 \\ - 4x - 7x = - 3 - 30 \\ - 11x = - 33 \\ x = 3$

f) 2(x + 3) - 5(2x + 1) = 12x - 19

$2(x + 3) - 5(2x + 1) = 12x - 19 \\ 2x + 6 - 10x - 5 = 12x - 19 \\ - 8x - 12x = - 19 - 1 \\ - 20x = - 20 \\ x = 1$

g) 3(2x + 3) + 2(3x + 2) = 9x + 4

$3(2x + 3) + 2(3x + 2) = 9x + 4 \\ 6x + 9 + 6x + 4 = 9x + 4 \\ 12x - 9x = 4 - 13 \\ 3x = - 9 \\ x = - 3$

h) 5(x - 2) - 2x - (6 + 7x) = 3(-x-1)

$5(x - 2) - 2x - (6 + 7x) = 3(-x-1) \\ 5x - 10 - 2x - 6 - 7x = - 3x - 3 \\ - 4x + 3x = - 3 + 16 \\ - x = 13 \\ x = - 13$

i) 4(x + 6) -6(x - 1) = 3x - 5

$4(x + 6) -6(x - 1) = 3x - 5 \\ 4x + 24 - 6x + 6 = 3x - 5 \\ - 2x - 3x = - 5 - 30 \\ - 5x = - 35 \\ x = 7$

j) 6(x + 2) - 2(2x + 3) + 4x = 36

$6(x + 2) - 2(2x + 3) + 4x = 36 \\ 6x + 12 - 4x - 6 + 4x = 36 \\ 6x = 36 - 6 \\ 6x = 30 \\ x = 5$

k) 3(x+2) -(4x + 1) = 2(4-x)

$3(x+2) -(4x + 1) = 2(4-x) \\ 3x + 6 - 4x - 4 = 8 - 2x \\ - x + 2x = 8 - 2 \\ - x = 6 \\ x = - 6$

l) 5(x - 2) + 4x - 3 = 6x +11

$5(x - 2) + 4x - 3 = 6x +11 \\ 5x - 10 + 4x - 3 = 6x + 11 \\ 9x - 6x = 11 + 13 \\ 3x = 24 \\ x = 8$

m) 5(x + 2) - (7 + 5x) = 3x

$5(x + 2) - (7 + 5x) = 3x \\ 5x + 10 - 7 - 5x = 3x \\ - 3x = - 3 \\ x = 1$

n) 5(x - 1) + 3x - 4 = 3x + 11

$5(x - 1) + 3x - 4 = 3x + 11 \\ 5x - 5 + 3x - 4 = 3x + 11 \\ 8x - 3x = 11 + 9 \\ 5x = 20 \\ x = 4$