Page 30 - 新思维数学活动用书8 样章

2.5 Constructing and solving equations

4 The diagram shows a rectangle. 4(x + 2)
Complete the workings to find the values of x and y.
6(y + 3) 30
4(x + 2) = 40 x + 2 × 4 40

40

x = – 2 ÷ 4 40 Tips

The lengths of
6(y + 3) = 30 y + 3 × 6 30
the rectangle

are the same, so
y = 30 4(x + 2) = 40.

Sometimes, you may have to solve an equation that has The widths of

the same letter on both sides of the = sign. the rectangle
are the same, so
Worked example 2.2 6(y + 3) = 30.

Solve 5x + 8 = 3x + 20

Answer
Subtract 3x from both sides: 5x − 3x + 8 = 3x − 3x + 20 Subtracting 3x from both

2x + 8 = 20 sides leaves no x on the right.

Then use a flow chart to solve 2x + 8 = 20 x × 2 + 8 20

12
x = 6 6 ÷ 2 – 8 20

5 Complete the workings to simplify these equations. Then solve the
equations by drawing a flow chart.

a 4x + 5 = x + 17 Subtract x from both sides: 4x − x + 5 = x − x + 17
3x + =
b 7x + 2 = 2x + 27 Subtract 2x from both sides: 7x − 2x + 2 = 2x − 2x + 27
x + =

c 10x − 4 = 8x + 12 Subtract 8x from both sides: 10x − 8x − 4 = 8x − 8x + 12
x − =

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