# maths ~~~~~~

1. x + 3 > 2

X = ______

2. x - 2 > 3

x = ______

3.Write each of the following in algebraic form :

(a) The sum of x and y ( x < y ) is multiplied by their difference .

(b) The square of the difference between x and 3y ( x > 3y ) .

4. 2 ( x + 1 ) > 4

X = _____

5. 7x - 9 > 9x + 7

x = ______

6.Danny has 14 model cars .

(a) As his mother is worried that he will spend too much money on model cars , she proposes the following to Danny :

" The maximum number of model cars that Danny can have is 20 . "

Let the total number of model cars that Danny can have be x .

( i ) Write an inequality to represent this situation .

( ii ) Hence find at most how many more model cars he can have .

(b) However , he makes the following counter - proposal :

" Apart from the condition stated above , I would like the total number of model cars to be greater than 17 . "

( i ) How many model cars can he have under this situation ?

( ii ) Hence find at least how many more model cars he can have .

Rating

1.

x + 3 > 2

x > -1

=====

2. x - 2 > 3

x > 5

=====

3.

(a)

(x + y)(y - x)

(b)

(x - 3y)²

=====

4.

2 ( x + 1 ) > 4

x + 1 > 2

x > 1

=====

5.

7x - 9 > 9x + 7

2x < -16

x < -8

=====

6.

(a)(i)

x ≤ 20

(a)(ii)

Let n be the number of model cars he can have.

x ≤ 20

14 + n ≤ 20

n ≤ 6

Hence, he can have at most 6 more model cars.

(b)(i)

17 < x ≤ 20

(b)(ii)

Let m be the number of model cars he can have.

x < 17

14 + m > 17

m > 3

Hence, he can have at least 3 more model cars.

2014-07-14 04:47:04 補充：

Amendment :

5.

(b)(ii)

Let m be the number of model cars he can have.

x < 17

14 + m > 17

m > 3

Hence, he can have at least 4 more model cars.

Source(s): 土扁, 土扁
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