Краткое пояснение: Упрощаем выражения, приводя подобные слагаемые и раскрывая скобки.
1) \[
3a + 14 + 5a - a + 7 = (3a + 5a - a) + (14 + 7) = 7a + 21
\]
2) \[
13 + 7x + 5 - 7 - x = (7x - x) + (13 + 5 - 7) = 6x + 11
\]
3) \[
24 + y + 2y - 12 - 4y = (y + 2y - 4y) + (24 - 12) = -y + 12
\]
4) \[
a + 2y + x - 3a - 6x - 4y = (a - 3a) + (2y - 4y) + (x - 6x) = -2a - 2y - 5x
\]
5) \[
-x + 5 - 4x - 9 = (-x - 4x) + (5 - 9) = -5x - 4
\]
6) \[
5 \cdot (3a - 4) = 5 \cdot 3a - 5 \cdot 4 = 15a - 20
\]
7) \[
2 \cdot (x - y + 7) = 2 \cdot x - 2 \cdot y + 2 \cdot 7 = 2x - 2y + 14
\]
8) \[
-3 \cdot (4x - 8y + 4 - 2x + 2y) = -3 \cdot (4x - 2x) - 3 \cdot (-8y + 2y) - 3 \cdot 4 = -3 \cdot 2x - 3 \cdot (-6y) - 12 = -6x + 18y - 12
\]
9) \[
5 \cdot (9x - 8z - 3 + 2z - 4 - 3x) = 5 \cdot (9x - 3x) + 5 \cdot (-8z + 2z) + 5 \cdot (-3 - 4) = 5 \cdot 6x + 5 \cdot (-6z) + 5 \cdot (-7) = 30x - 30z - 35
\]
10) \[
7 \cdot (8x - 4y) - (11x + 8y) = 7 \cdot 8x - 7 \cdot 4y - 11x - 8y = 56x - 28y - 11x - 8y = (56x - 11x) + (-28y - 8y) = 45x - 36y
\]
11) \[
-12 \cdot (-4x + 2y) + (15y - 17x) = -12 \cdot (-4x) - 12 \cdot 2y + 15y - 17x = 48x - 24y + 15y - 17x = (48x - 17x) + (-24y + 15y) = 31x - 9y
\]
12) \[
3.6 \cdot (5x - 3y) - 4.1 \cdot (2y - 3x) = 3.6 \cdot 5x - 3.6 \cdot 3y - 4.1 \cdot 2y + 4.1 \cdot 3x = 18x - 10.8y - 8.2y + 12.3x = (18x + 12.3x) + (-10.8y - 8.2y) = 30.3x - 19y
\]
13) \[
-2.1 \cdot (8.5z + 3b) + 3.1 \cdot (2z - 4b) = -2.1 \cdot 8.5z - 2.1 \cdot 3b + 3.1 \cdot 2z - 3.1 \cdot 4b = -17.85z - 6.3b + 6.2z - 12.4b = (-17.85z + 6.2z) + (-6.3b - 12.4b) = -11.65z - 18.7b
\]
Ответ: 1) 7a + 21; 2) 6x + 11; 3) -y + 12; 4) -2a - 2y - 5x; 5) -5x - 4; 6) 15a - 20; 7) 2x - 2y + 14; 8) -6x + 18y - 12; 9) 30x - 30z - 35; 10) 45x - 36y; 11) 31x - 9y; 12) 30.3x - 19y; 13) -11.65z - 18.7b