Page 51 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

Continued

b 3(x + 3) = 24 The two lengths must be equal, so construct an equation by writing
one length equal to the other.
3x + 9 = 24 First, multiply out the brackets.

3x + 9 − 9 = 24 − 9 Then use inverse operations to solve the equation.
Start by subtracting 9 from both sides.
3x = 15 Simplify both sides of the equation.
15
x = = 5 Divide 15 by 3 to find the value of x.
3
5y − 4 = 3y + 8 The two widths must be equal, so write one width equal

to the other.
5y − 4 − 3y = 3y + 8 − 3y Rewrite the equation by subtracting 3y from both sides.
2y − 4 = 8 Simplify.
2y − 4 + 4 = 8 + 4 Use inverse operations to solve the equation. Start by adding
4 to both sides.

2y = 12 Simplify both sides of the equation.
12
y = = 6 Divide 12 by 2 to work out the value of y.
2

Exercise 2.5

1 Write if each of the following is a formula, an expression or
an equation.
a 3y + 7 = 35 b 6(x + 5)
c T = 3a − 8d d 9u − vw
2
2 Copy and complete the workings to solve these equations.
a 3x + 5 = 26 (subtract 5 from both sides) 3x + 5 − 5 = 26 − 5
(simplify) 3x =

(divide both sides by 3) x =
3
(simplify) x =
b 4(x − 3) = 24 (multiply out the brackets) 4x − 12 = 24

(add 12 to both sides) 4x − 12 + 12 = 24 + 12

(simplify) 4x =

(divide both sides by 4) x =
4
(simplify) x =

50