中一數學問題數條!謝

1. Solve 6(x + 3) - (3x - 8) = 5

6(x + 3) - (3x - 8) = 5
6x + 18 - 3x + 8 = 5
3x = -21
x = -7


= = = = =
2. Solve (y - 1)/9 = (2y + 1)/6

(y - 1)/9 = (2y + 1)/6
6(y - 1) = 9(2y + 1)
2(y - 1) = 3(2y + 1)
2y - 2 = 6y + 3
4y = -5
y = -5/4


= = = = =
3. The side of a square is 12 cm long. If each side of the square decrease by 20%, find:
(a) the new areaofthe square,
(b) the percentage decrease in its area.

(a)
New area of the square
= [12(1 - 20%)]² cm²
= 92.16 cm²

(b)
The percentage decrease in area
= [(12² - 92.16)/12²] * 100%
= 36%


= = = = =
4. Simplify (14y^-7+5y)(5-6y-3y^) and arrange theterms in descending powers of y.

If ^ means "square", the answer is as follows. If not, what does it means?

(14y² - 7 + 5y)(5 - 6y - 3y²)
= 14y²(5 - 6y - 3y²) - 7(5 - 6y - 3y²) + 5y(5 - 6y - 3y²)
= 70y² - 84y³ - 42y⁴ - 35 + 42y + 21y² + 25y - 30y² - 15y³
= - 42y⁴ - 99y³ + 61y² + 67y- 35


= = = = =
5. Expand (4x + 5y)(-3y + 7x)

(4x + 5y)(-3y + 7x)
= 4x(-3y + 7x) + 5y(-3y + 7x)
= -12xy + 28x² - 15y² + 35xy
= 28x² + 23xy - 15y²