Page 32 - 新思维数学活动用书8 样章

2.5 Constructing and solving equations

8 Work out the value of x in each isosceles trapezium.
All measurements are in centimetres. Show how you can check
your answers are correct.
a 7(x – 2) 3x + 6 b 3x + 6 6(x – 1)

c 2(x + 6) 9(x – 1)

9 Work out the value of the letters in each diagram.
All measurements are in centimetres.
a 10c − 3 b f
10 + 58
d 8
5 − 2
5(e + 2) 45
17
63
c 6j + 1

3i + 5 2i + 10

5j + 5
10 For each part of this question
i Write an equation to represent the problem.

ii Solve the equation.
a Arti thinks of a number. He divides it by 2 then subtracts 9.
The answer is 5.
What number did Arti think of?

b Han thinks of a number. She multiplies it by 4 then subtracts 1.
The answer is the same as 3 times the number plus 6.
What number did Han think of?

c Danni thinks of a number. She subtracts 2 then multiplies the
result by 8. The answer is the same as subtracting 5 from the
number then multiplying by 16.
What number did Danni think of?

Challenge

11 The total area of this rectangle is 52 cm .
2
a Write an equation to represent the problem. 4 cm

b Solve the equation to work out the value of y.
2y cm 7 cm
c Show how you can check your answer is correct.

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