Page 58 - 新思维数学学生用书8 样章

2.6 Inequalities

2 Write each statement as an inequality. Part a has been done for you.

a y is greater than or equal to 3 and less than 17 3 < y < 17
b y is greater than 15 and less than 25
c y is greater than −2 and less than or equal to 5
d y is greater than or equal to −9 and less than

or equal to −3
3 Copy each number line and show each inequality on the
number line.
a 4 < x < 7 b 6 ≤ x ≤ 9

3 4 5 6 7 8 5 6 7 8 9 10

c −4 < x ≤ 1 d −2 ≤ x < 2

−5 −4 −3 −2 −1 0 1 2 −3 −2 −1 0 1 2 3
4 Write the inequality that each of these number lines shows.

Use the letter x.
a b
11 12 13 14 15 16 17 0 1 2 3 4 5
c d

−3 −2 −1 0 1 2 0 2 4 6 8 10 12

Think like a mathematician

5 Sofia and Zara are looking at the inequality x > 5.

In pairs or small groups, discuss Sofia’s and Zara’s comments.

The inequality The inequality
x > 5 is equivalent to x > 5 is equivalent
2x > 10. to x − 2 > 3.

a How can you show that Sofia and Zara are correct? Tip
b Write two different inequalities that are equivalent

to x > 5. Remember that
c Is it possible to say how many different inequalities ‘equivalent to’
there are that are equivalent to x > 5? Explain your means ‘the same
answer. as’ or ‘equal to’.

57