Page 34 - 新思维数学活动用书7 样章

2.5 Constructing and solving equations

Challenge

9 The diagram shows a rectangle.
The width of the rectangle is 2x − 3y cm. 2x – 3y cm
The length of the rectangle is 12 cm.
Write an expression, in its simplest form, for the: 12 cm

a area of the rectangle b perimeter of the rectangle.
10 Expand and simplify these expressions.
a 3(x + 2) + 4x b 4(9 + x) − 24

c 5(2x − 2) + x + 17 d 6(3x − 4) −8x + 4 Tip
e 4(x + 4) + 7(x + 1) f 8(5 + 2x) + 3(x − 6) ≡ means ‘is
11 Show that 4(2x + 7) + 3(6x − 5) ≡ 13(2x + 1). equivalent to’ or
12 Work out the missing numbers in these expansions. ‘is the same as’.

−
a 9 3x+ 2) = 3( x+ ) b 5 86 ) = 10( − ) z
(
z
(
13 Work out the missing numbers in these expansions.
All the numbers are in the cloud. Only use each number once. 2 3 4 6
a ( 2x+ ) = 8x+ b 5( x − ) = x − 35 7 8 9 14
c ( 6y − 10) = y − 80 d 7( y+ ) = y+ 42 15 36 48

2.5 Constructing and solving equations

When you solve an equation, you find the value of the unknown letter. Key words
You can use a flow chart like this to solve an equation using inverse
operations. inverse operation

Solve: x + 5 = 12 x +5 12 solve
So x = 7 7 −5 12
Tip
Reverse the flow
Exercise 2.5 chart to work out

the value of x.
Focus

1 Write down the missing numbers.
a + 4 = 6 b + 1 = 6 c + 2 = 10

d 8 − = 5 e 9 − = 2 f 17 − = 10

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