Page 57 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

Tip
If you see the inequality 3 ≤ x < 9, this means that x is greater than or This closed

equal to 3 and is also less than 9. This inequality represents a closed interval includes
interval. You can show this on a number line like this.
the endpoints 3
and 9.
2 3 4 5 6 7 8 9 10

Worked example 2.6 Tip

a i Show the inequality 2 ≤ x < 6 on a number line. Remember that

ii List the possible integer values for. an integer is a
b i Show the inequality −5 < y ≤ −1 on a number line. whole number.
ii List the possible integer values for y.

Answer

a i Use a closed circle for the ≤ sign and start the
1 2 3 4 5 6 7 8 line at 2.
Extend the line to 6, where you use an open
circle for the < sign.

ii 2, 3, 4, 5 x is greater than or equal to 2, so 2 is the
smallest integer.
x is less than 6, so 5 is the greatest integer.
b i Use an open circle for the < sign and start the
−6 −5 −4 −3 −2 −1 0 line at −5.
Extend the line to −1, where you use a closed
circle for the ≤ sign.
ii −4, −3, −2, −1 y is greater than −5, so −4 is the smallest
integer.
y is less than or equal to −1, so −1 is the
greatest integer.

Exercise 2.6

1 Write in words what each of these inequalities means.

Part a has been done for you.
a 6 < x < 11 x is greater than 6 and less than 11
b 12 ≤ x ≤ 18
c 0 < x ≤ 20
d −9 ≤ x < −1

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