math f1

1) 6[2x-3(x+1)]=2x-10

6(2x - 3x - 3) = 2x - 10

-6x - 18 = 2x - 10

-8 = 2x + 6x

8x = -8

x = -1

2) for two consecutive even numbers,3 times the large number is 22 more than 2 times the smaller number.find the two numbers.

Sol :

Let the smaller number be y.

3(y + 2) = 2y + 22

3y + 6 = 2y + 22

y = 16

So, the larger even number is 16 + 2 = 18, the smaller even number is 16.

3) The total weight of 130 packs of sugar is 134 kg.some of them weigh0.5kg each and the others weigh2 kg each. how many packs of sugar weigh 0.5 kg each?

Sol :

Let the number of pack of sugar of 0.5kg and 2kg be y and z respectively.

0.5y + 2z = 134.....(1)
y + z = 130.....(2)

(2) : y = 130 - z.....(3)

Subst.(3) into (1) : 0.5(130 - z) + 2z = 134
65 - 0.5z + 2z = 134
1.5z = 69
z = 46.....(4)

Put (4) into (2)
y = 84

So, there are 84 packs of sugar weigh 0.5 kg.

4) 2[(3x-4)2x]=x+10
2(6x^2 - 8x) = x + 10
12x^2 - 16x = x + 10
12x^2 - 17x - 10 = 0 ← 很怪耶…

是不是?
2[(3x-4)+2x]=x+10
2(5x - 4) = x + 10
10x - 8 = x +10
9x = 18
x = 2

5) 5[2(x-3.2)+x]=x-4
5(2x - 6.4 + x) = x - 4
10x - 32 + 5x = x - 4
15x - 28 = x
14x = 28
x = 2

6) 2[x-(2-3x)=13x+4
2(x - 2 + 3x) = 13x + 4
2x - 4 + 6x = 13x + 4
8x = 13x + 8
-5x = 8
x = -8 / 5

希望能夠幫到大大！


圖片參考：http://imgcld.yimg.com/8/n/HA00943178/o/700912280140413873388470.jpg

1. 6[2x-3(x+1)]=2x-10

6 [ 2x - 3x - 3 ] = 2x - 10
6 [ -x - 3 ] = 2x - 10
-6x - 18 = 2x - 10
2x + 6x = -18 + 10
8x = -8
x = -1

2. Let x and ( x + 2 ) are the TWO consecutive even numbers

3 x = 2 ( x + 2 ) + 22
3x - 2x = 22 + 4
x = 26

so the TWO consecutive even numbers are 26 and 28

3. 0.5 X + 2(130-X) = 134
0.5X - 2X = 134 - 260
-1.5X = -126
1.5X = 126
X = 84

There are 84 packs of 0.5 Kg sugar.