Раскройте скобки и приведите подобные слагаемые. Вариант 5.

Решение:

1. A1. \( 4(x+2)-3(5-x)-x-3 = 4x + 8 - 15 + 3x - x - 3 = (4x + 3x - x) + (8 - 15 - 3) = 6x - 10 \)
2. A2. \( 3(x+3)-4(3-x)-(4+3)x-3 = 3x + 9 - 12 + 4x - 7x - 3 = (3x + 4x - 7x) + (9 - 12 - 3) = 0x - 6 = -6 \)
3. A3. \( 5(x+4)-(5-x)-x-3 = 5x + 20 - 5 + x - x - 3 = (5x + x - x) + (20 - 5 - 3) = 5x + 12 \)
4. A4. \( 4(x+1)-5(5-x)-(5+4)x-1 = 4x + 4 - 25 + 5x - 9x - 1 = (4x + 5x - 9x) + (4 - 25 - 1) = 0x - 22 = -22 \)
5. A5. \( 2(x+2)-5(4-x)-(5+2)x-3 = 2x + 4 - 20 + 5x - 7x - 3 = (2x + 5x - 7x) + (4 - 20 - 3) = 0x - 19 = -19 \)
6. A6. \( 4(x+1)-4(3-x)-x-5 = 4x + 4 - 12 + 4x - x - 5 = (4x + 4x - x) + (4 - 12 - 5) = 7x - 13 \)
7. A7. \( 2(x+4)-(2-x)-(1+2)x-1 = 2x + 8 - 2 + x - 3x - 1 = (2x + x - 3x) + (8 - 2 - 1) = 0x + 5 = 5 \)
8. A8. \( x+4-2(5-x)-x-4 = x + 4 - 10 + 2x - x - 4 = (x + 2x - x) + (4 - 10 - 4) = 2x - 10 \)
9. A9. \( x+5-(2-x)-(1+1)x-1 = x + 5 - 2 + x - 2x - 1 = (x + x - 2x) + (5 - 2 - 1) = 0x + 2 = 2 \)
10. A10. \( 5(x+1)-2(5-x)-x-3 = 5x + 5 - 10 + 2x - x - 3 = (5x + 2x - x) + (5 - 10 - 3) = 6x - 8 \)

Ответ:

• A1. \( 6x - 10 \)
• A2. \( -6 \)
• A3. \( 5x + 12 \)
• A4. \( -22 \)
• A5. \( -19 \)
• A6. \( 7x - 13 \)
• A7. \( 5 \)
• A8. \( 2x - 10 \)
• A9. \( 2 \)
• A10. \( 6x - 8 \)