Ответы
1) 2x+13 = 22+3x
2x-3x = 22-13
-x = 9
x = -9
Проверка:
2x+13 = 2·(-9)+13 = -18+13 = -5
22+3x = 22+3·(-9) = 22-27 = -5
-5 = -5
2) 3x-(10-9x) = 22x
3x-10+9x = 22x
12x-10 = 22x
12x-22x = 10
-10x = 10
x = -1
Проверка:
3x-(10-9x) = 3·(-1)-(10-9·(-1)) = -3-(10+9) = -3-19 = -22
22x = 22·(-1) = -22
3) 21x+45 = 15+14x
21x-14x = 15-45
7x = -30
x = -30/7
Проверка:
21x+45 = 21·(-30/7)+45 = -3·30+45 = -90+45 = -45
15+14x = 15+14·(-30/7) = 15+2·(-30) = 15-60 = -45
-45 = -45
4) 13x+40 = 2x+7
13x-2x = 7-40
11x = -33
x = -3
Проверка:
13x+40 = 13·(-3)+40 = -39+40 = 1
2x+7 = 2·(-3)+7 = -6+7 = 1
1 = 1
5) 25-(7-2x) = 5x
25-7+2x = 5x
18+2x = 5x
2x-5x = -18
-3x = -18
x = 6
Проверка:
25-(7-2x) = 25-(7-2·6) = 25-(7-12) = 25-(-5) = 25+5 = 30
5x = 5·6 = 30
30 = 30
6) 5-3x = 2x-8
-3x-2x = -8-5
-5x = -13
x = 13/5
Проверка:
5-3·13/5 = 5-39/5 = 5-7 4/5 = -2 4/5
2x-8 = 2·13/5-8 = 26/5-8 = 5 1/5-8 = -2 4/5
-2 4/5 = -2 4/5
7) 2x+40 = x+14
2x-x = 14-40
x = -26
Проверка:
2x+40 = 2·(-36)+40 = -52+40 = -12
x+14 = -26+14 = -12
-12 = -12
8) 14x+5x = 4x+3
19x = 4x+3
19x-4x = 3
15x = 3
x = 3/15 = 1/5
Проверка:
14x+5x = 14·1/5+5·1/5 = 14/5+5/5 = 19/5
4x+3 = 4·1/5+3 = 4/5+15/5 = 19/5
19/5 = 19/5
9) -15x+31 = -7+4x
-15x-4x = -7-31
-19x = -38
x = 2
Проверка:
-15x+31 = -15·2+31 = -30+31 = 1
-7+4x = -7+4·2 = -7+8 = 1
1 = 1
10) 3x-12 = 8x+13
3x-8x = 13+12
-5x = 25
x = -5
Проверка:
3x-12 = 3·(-5)-12 = -15-12 = -27
8x+13 = 8·(-5)+13 = -40+13 = -27
-27 = -27