Page 53 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

Think like a mathematician

4 Marcus and Sofia are discussing what equation to
write to answer this question. 2y +7 5y − 17

The diagram shows an isosceles triangle.
All measurements are in centimetres.
Work out the value of y.

I would write
As the triangle is an the equation
isosceles triangle, the 5y − 17 = 2y + 7
two sides shown are equal because I think
in length. So I would this is easier to
write the equation solve.
2y + 7 = 5y − 17.

What do you think? Does it matter which way round you write the equation?
Work with a partner to discuss and explain your answers.

5 Work out the value of x in each isosceles triangle. Tip

All measurements are in centimetres.
a b Think carefully
6x − 3 9 about which way
27 x + 20
2
round you write
c your equations.
x + 35 5x − 13

Think like a mathematician

6 Look back at your answers to Question 5.

Discuss with a partner how you can check your value for x in each part.

7 Work out the value of y in each shape. All measurements are in centimetres.
Show how to check your answers are correct.

a 4(y − 3) 2y + 2 b 8y − 5 c 2(y + 6) 4(y − 3)

3(y + 5)

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