Page 60 - 新思维数学学生用书8 样章

2.6 Inequalities

10 Write true (T) or false (F) for each statement.
Part a has been done for you.
a 7 ≥ y > 3 means the same as 3 < y ≤ 7 T
b 15 > y ≥ 5 means the same as 5 < y ≤ 15
c 10 ≥ y ≥ −6 means the same as −6 ≤ y ≤ 10
d 8 > y ≥ −8 means the same as −8 < y ≤ 8

11 Samir combines two inequalities into one.

The two inequalities m < 10 and m > 2 can be combined like this:
Step 1:

m > 2 is the same as 2 < m
Step 2:
The two inequalities are now 2 < m and m < 10
I can write these as one inequality: 2 < m < 10

I can use a number line to help me:

m > 2 or 2 < m m < 10

0 2 4 6 8 10 12 0 2 4 6 8 10 12

2 < m < 10

0 2 4 6 8 10 12

a Use Samir’s method to combine each pair of inequalities into one.
Use a number line to help if you want to.

i m < 15 and m > 8
ii m ≤ 10 and m > 7
iii m > 0 and m < 6
b Is it possible to write m > 14 and m < 8 as one inequality?
Give a reason for your answer.
Discuss your answer with a partner.

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