Page 59 - 新思维数学学生用书8 样章

2 Expressions, formulae and equations

6 Copy and complete these equivalent inequalities.

a x > 8 is equivalent to 3x > b x < 3 is equivalent to x < 15
c y > 7 is equivalent to y + 3≥ d y ≤ 2 is equivalent to y − 4 ≤
7 This is part of Ryan’s homework.

Question
Use the inequality 12 ≤ x < 18 to write
i the smallest integer that x could be

ii the largest integer that x could be
iii a list of the integer values that x could be.
Answer
i smallest integer is 13
ii largest integer is 18

iii x could be 13, 14, 15, 16, 17, 18

a Explain the mistakes Ryan has made and write the correct solutions.
b Discuss your answers to part a with a partner.
Make sure you have corrected all of Ryans’s mistakes.

8 For each of these inequalities, write
i the smallest integer that y could be
ii the largest integer that y could be

iii a list of the integer values that y could be.
a 3 < y < 8 b 4 < y ≤ 7 c 0 ≤ y < 6 d −10 ≤ y ≤ −6

Think like a mathematician

9 Arun and Sofia are looking at the inequality 2 < y < 9.
In pairs or small groups discuss Arun’s and Sofia’s comments.

I think the I think the
inequality 2 < y < 9 inequality 2 < y < 9
can be written as can be written as
9 > y > 2. 2 > y > 9.

What do you think? Explain your answers.

58