Решение уравнения с модулями: А) |x+6|+|x-7|+|x+11|=25 Б) |х+4|+|х-9|+|х+8|+|х-5|=17 В) |3t-6|+|4t+12|+|2t-18|-|5t+10|=37

А) |x + 6|+|x - 7| + |x + 11| = 25;|x + 6| = 25 -|x - 7| - |x + 11|;1) x + 6 = 25 -|x - 7| - |x + 11|;x - 19 = -|x - 7| - |x + 11|; x - 19 + |x - 7| = - |x + 11|; - x + 19 - |x - 7| = |x + 11|;a) x + 11 = - x + 19 - |x - 7|;x + 11 = - x + 19 - |x - 7|;x + 11 + x - 19 = - |x - 7|; 2 * x - 8 = - |x - 7|;8 - 2 * x = |x - 7|;x - 7 = 8 - 2 * x, x + 2 * x = 8 + 7, 3 * x = 15, x = 5;x - 7 = - 8 + 2 * x, x - 2 * x = - 8 + 7, - x = - 1, x = 1;b) x + 11 = x - 19 + |x - 7|;x + 11 - x + 19 = |x - 7|;|x - 7| = 30;x - 7 = 30, x = 37;x - 7 = - 30, x = - 23;2) - x - 31 = -|x - 7| - |x + 11|;- x - 31+ |x - 7| = - |x + 11|; + x + 31 -|x - 7| = |x + 11|; a) x + 11 = + x + 31 -|x - 7|;-|x - 7| = - 20;|x - 7| = 20;x - 7 = 20, x = 27;x - 7 = - 20, x = - 13;b) - x - 11 = + x + 31 -|x - 7|;x + 11 + x + 31 = |x - 7|;|x - 7| = 2 * x + 42;x - 7 = 2 * x + 42, x - 2 * x = 42 + 7, - x = 49, x = - 49;x - 7 = - 2 * x - 42, x + 2 * x = - 42 + 7, 3 * x = - 35, x = - 35 / 3;Ответ: х = 5, x = 1, x = 37, x = - 23, x = 27, x = - 13, x = - 49, x = - 35 / 3. Б) |х + 4| + |х - 9| + |х + 8| + |х - 5| = 17;{ х + 4 + |х - 9| + |х + 8| + |х - 5| = 17; - х - 4 + |х - 9| + |х + 8| + |х - 5| = 17;{ х + 4 + х - 9 + |х + 8| + |х - 5| = 17;х + 4 - x + 9 + |х + 8| + |х - 5| = 17; - х - 4 + х - 9 + |х + 8| + |х - 5| = 17; - х - 4 - x + 9 + |х + 8| + |х - 5| = 17;{ х + 4 + х - 9 + х + 8 + |х - 5| = 17;х + 4 + х - 9 - x - 8 + |х - 5| = 17;х + 4 - x + 9 + х + 8 + |х - 5| = 17;х + 4 - x + 9 - x - 8 + |х - 5| = 17; - х - 4 + х - 9 + х + 8 + |х - 5| = 17; - х - 4 + х - 9 - x - 8 + |х - 5| = 17; - х - 4 - x + 9 + x + 8 + |х - 5| = 17; - х - 4 - x + 9 - x - 8 + |х - 5| = 17;{ х + 4 + х - 9 + х + 8 + х - 5 = 17;х + 4 + х - 9 + х + 8 - x + 5 = 17;х + 4 + х - 9 - x - 8 + х - 5 = 17;х + 4 + х - 9 - x - 8 - x + 5 = 17;х + 4 - x + 9 + х + 8 + х - 5 = 17;х + 4 - x + 9 + х + 8 - x + 5 = 17;х + 4 - x + 9 - x - 8 + х - 5 = 17;х + 4 - x + 9 - x - 8 - x + 5 = 17; - х - 4 + х - 9 + х + 8 + х - 5 = 17; - х - 4 + х - 9 + х + 8 - x + 5 = 17; - х - 4 + х - 9 - x - 8 + х - 5 = 17; - х - 4 + х - 9 - x - 8 - x + 5 = 17; - х - 4 - x + 9 + x + 8 + х - 5 = 17; - х - 4 - x + 9 + x + 8 - x + 5 = 17; - х - 4 - x + 9 - x - 8 + x - 5 = 17; - х - 4 - x + 9 - x - 8 - x + 5 = 17; { 4 * x - 2 = 17; 2 * x + 8 = 17;2 * x- 18 = 17;2 * x + 16 = 17;- 2 * x + 10 = 17;2 * x - 10 = 17;- 2 * x - 16 = 17;- 2 * x + 18 = 17; - 2 * x - 8= 17;- 4 * x + 2 = 17;{ x = 19 / 4;x = 9 / 2;x = 35 / 2;x = 1 / 2;x = - 7 / 2;x = 27 / 2;x = - 33 / 2;x = 1 / 2;x = - 25 / 2;x = - 15 / 2; В) |3t - 6| + |4t + 12| + |2t - 18|- |5t + 10| = 37;{ 3t - 6 + |4t + 12| + |2t - 18|- |5t + 10| = 37;- 3t + 6 + |4t + 12| + |2t - 18|- |5t + 10| = 37;{ |4t + 12| + |2t - 18|- |5t + 10| = 43 - 3 * t; |4t + 12| + |2t - 18|- |5t + 10| = 31 + 3 * t;{ 4t + 12 + |2t - 18|- |5t + 10| = 43 - 3 * t;-4t - 12 + |2t - 18|- |5t + 10| = 43 - 3 * t;4t + 12 + |2t - 18|- |5t + 10| = 31 + 3 * t; -4t - 12 + |2t - 18|- |5t + 10| = 31 + 3 * t; { |2t - 18|- |5t + 10| = 31 - 7 * t; |2t - 18|- |5t + 10| = 55 + t; |2t - 18|- |5t + 10| = 19 - t; |2t - 18|- |5t + 10| = 43 + 7 * t; { 2t - 18- |5t + 10| = 31 - 7 * t;-2t + 18- |5t + 10| = 31 - 7 * t;2t - 18- |5t + 10| = 55 + t;-2t +18- |5t + 10| = 55 + t;2t - 18- |5t + 10| = 19 - t; -2t + 18 - |5t + 10| = 19 - t; 2t - 18- |5t + 10| = 43 + 7 * t; -2t +18 - |5t + 10| = 43 + 7 * t;{ 9 t - 49 = |5t + 10|;5t -13 = |5t + 10|;t - 73 =|5t + 10|;3t + 1 =|5t + 10|; -t - 1 = |5t + 10|; -5t - 61 = |5t + 10|; -9t - 25 = |5t + 10|; { 9 t - 49 = 5t + 10; 9 t - 49 = -5t - 10;5t -13 = 5t + 10; 5t -13 = -5t - 10;t - 73 = 5t + 10; t - 73 =-5t - 10;3t + 1 = 5t + 10; 3t + 1 = -5t - 10;-t - 1 = 5t + 10; -t - 1 = -5t - 10;-5t - 61 = 5t + 10; -5t - 61 = -5t - 10; -9t - 25 = 5t + 10; -9t - 25 = -5t - 10;{ t = 59 / 4; t = 39 / 14;5t -13 = -5t - 10;t = - 83 / 4 t =63 / 6t = - 9 / 2;t =- 11 / 8;t = - 11 / 4;t = - 9 / 4;t = - 71 / 14;t = - 35 / 14; t = - 15 / 4.