Page 55 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

11 The diagram shows the sizes of the two equal angles in an
isosceles triangle.

(4x − 6) ° (2x + 18) ° Tip

a Write an equation to represent the problem.
b Solve your equation to find the value of x. Start by expanding
c Work out the size of each of the angles in the triangle. the brackets and

12 Solve these equations. simplifying the left
Use the Tip box to help. hand side.
a 5(2x + 3) + 2(x − 4) = 31 2 y is the same as
3
b 4(3x − 1) − 3(5 − 2x) = 35 2 × y so start by

c 2 y = 8 3
3 multiplying both
d 3 y += sides by 3.
119
5

Question
Solve the equation 4(2b – 3) = −8b
Answer
Divide both sides by 4 4(2b − 3) = −8b → 2b – 3 = −2b
4 4
Add 3 to both sides 2b – 3 + 3 = −2b + 3 → 2b = −2b + 3
Add 2b to both sides 2b + 2b = −2b + 2b + 3 → 4b = 3
3
Divide both sides by 4 4b = → b = 3
4 4 4

13 This is part of Mo’s homework.
You can see that instead of multiplying out the bracket,

Mo’s first step is to divide both sides of the equation by 4.
Use Mo’s method to solve these equations.
(
)
2
a 6(3a + 4) = 12a b 5(4c − 9) = 25 c 3 d + 4 = 18
5

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