Page 50 - 新思维数学学生用书8 样章

2.5 Constructing and solving equations

2.5 Constructing and solving equations

In this section you will … Key word

• write and solve equations. construct

You already know the difference between a formula, an expression and
an equation.

Remember Examples
A formula is a rule that shows the relationship F = ma
between two or more quantities (variables). It v = u + 10t
must have an equals sign.
An expression is a statement that involves one 3x − 7
or more variables, but does not have an equals a + 2b
2
sign.
An equation contains an unknown number. It 3x − 7 = 14
must have an equals sign, and it can be solved
to find the value of the unknown number. 4 = 6y + 22

When you are given a problem to solve, you may need to construct, or
write, an equation.

Worked example 2.5

a Write if each of the following is a formula, an expression or an equation.
i 4c + 3e ii P = 8h + b iii 9k − 2 = 16
b The diagram shows a rectangle. 3(x + 3) cm
Work out the values of x and y.
5y − 4 cm 3y + 8 cm

24 cm

Answer
a i expression 4c + 3e involves two variables but does not have an equals sign.

ii formula P = 8h + b is a rule showing the relationship between three
quantities, P, h and b.

iii equation 9k − 2 = 16 contains an unknown number, k, it has an equals sign,
and it can be solved to find the value of k.

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