Page 56 - 新思维数学学生用书7 样章

2.6 Inequalities

Worked example 2.6

a i Show the inequality x > 5 on a number line.
ii What is the smallest integer that x could be? Remember that an integer is a

iii List the integer values that x could be. whole number.
b i Show the inequality y < 2 on a number line.
ii What is the largest integer that y could be?
iii List the integer values that y could be.

Answer
a i You use an open circle for the > sign, and start

3 4 5 6 7 8 9 the line at the number 5.
The line goes to the right because it is greater
than.

ii 6 x is greater than 5, so 6 is the smallest number.
iii 6, 7, 8, 9, 10, … You cannot list all of the integers because the
list goes on forever, so list the first five and
write ‘…’ (called ellipses) to show that the list
goes on forever.

b i You use an open circle for the < sign, and start
the line at the number 2.
–1 0 1 2 3 4
The line goes to the left because it is less than.
ii 1 y is less than 2, so 1 is the largest number.

iii 1, 0, −1, −2, −3, … You cannot list all of the integers because the
list goes on forever, so list the first five and
write ‘…’ to show that the list goes on forever.

Exercise 2.6

1 Write in words what each of these inequalities means. The first one
has been done for you.
a x < 10 x is less than 10

b x > 10
c x < −4
d x > −4

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