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Contents

- 1 Solutions for Lesson 8 Practice Questions
- 1.1 Intervals
- 1.2 Absolute Value
- 1.3 Distance on the Number Line
- 1.4 Strict Inequality
- 1.5 Prove Me Wrong
- 1.6 And or Or
- 1.7 Drug Variation 1
- 1.8 Drug Variation 2
- 1.9 Drug Variation 3
- 1.10 Drug Variation 4
- 1.11 Challenge

Write the regions marked on the lines in interval notation.

Give the value of each of the following without the absolute value signs.

a)

b)

c)

d)

e)

Write an expression to show that the distance...

a) between

and on a number line is equal to .or

b) between

and on a number line is equal to .or

If

, then...a) we can equivalently say

can equal any number up to and including .false

b) we can equivalently say

can equal any number up to and including .false

c) we can equivalently say

can equal any number up to and including .false

d) we can’t give a maximum value that

can equal because whatever number we choose, we can always find a number larger than that that is still smaller than .true

Suppose I claim that

means that can be any number up to and including .a) Prove me wrong by providing an example of a number which satisfies the inequality but is closer to

than to .Your answer can be any number that is greater than

but less than . Example:

b) So now I claim that your answer is the largest that

can be. Prove me wrong again by providing another number closer to than your number is.Your answer can be any number that is less than 10 but greater than the answer you put for part a). Since I put

in part a), I could put something like here.

c) If we carry on, will I eventually find the largest number possible that is *prove* in the box, and if not, put *largest*.

prove

Mark the regions on the number lines that satisfy the inequalities given.

a)

andb)

orAccording to the site Science Based Medicine, “Most regulators worldwide have decided that a 20% variation [in the active ingredient of a tablet] is generally not clinically significant.”

Acetylsalicylic acid is a painkiller originally derived from the bark of a willow tree. It’s often sold under the trade name ‘aspirin’. In the USA, a tablet of this drug usually contains 325 mg of active ingredient, that is, of acetylsalicylic acid rather than any additional ingredients. In the UK, a tablet usually contains 300 mg.

According to the information above, by how many milligrams (mg) can the amount of active ingredient vary...

a) in the USA tablet?

65 mg

b) in the UK tablet?

60 mg

According to the site Science Based Medicine, “Most regulators worldwide have decided that a 20% variation [in the active ingredient of a tablet] is generally not clinically significant.”

Acetylsalicylic acid is a painkiller originally derived from the bark of a willow tree. It’s often sold under the trade name ‘aspirin’. In the USA, a tablet of this drug usually contains 325 mg of active ingredient, that is, of acetylsalicylic acid rather than any additional ingredients. In the UK, a tablet usually contains 300 mg.

Sometimes, the variation is written as the standard amount

amount it’s allowed to vary, where means plus or minus. How would you write this for...c) USA

d) UK

According to the site Science Based Medicine, “Most regulators worldwide have decided that a 20% variation [in the active ingredient of a tablet] is generally not clinically significant.”

Acetylsalicylic acid is a painkiller originally derived from the bark of a willow tree. It’s often sold under the trade name ‘aspirin’. In the USA, a tablet of this drug usually contains 325 mg of active ingredient, that is, of acetylsalicylic acid rather than any additional ingredients. In the UK, a tablet usually contains 300 mg.

Suppose you have a tablet. It contains

milligrams of active ingredient. How can you write that the difference between and the standard amount for each tablet is at most the variation?e) USA

f) UK

USA:

UK:

Either by solving the inequalities in the previous question, or by thinking about the question, write the interval of values for

using inequalities.e) USA

and

and

and

f) UK

and

and

and

Considering the conditions given, write the following without the absolute value signs. For example, if

, then is negative, so .a)

whereb)

wherec)

where