Problem Set : Inequalities in One Variable
4:42 AM
Muhammad Yusuf
, Posted in
1. The
average of a set of n integers is 10. If we remove the integer 2
from this set, the average of the remaining integers is 14. What is the value
of n?
2. In a
bin at the Cayley Convenience Store, there are 200 candies. Of these candies,
90% are black and the rest are gold. After Matilda eats some of the black
candies, 80% of the remaining candies in the bin are black. How many black
candies did Matilda eat?
3. The five
expressions 2x + 1, 2x - 3, x + 2, x + 5 and x - 3 can be
arranged in a different order so that the sum of the first three expressions is
4x+3 and the sum of the last three expressions is
4x + 4. What is the middle expression in the new
list?
4. Solve
5x - 2 ≤ 3x - 10 and
sketch your solution.
5. Solve
10 - 7x < -4x - 9 and
sketch your solution.
6. Solve -1/2(2 + 5x) ≥ 2/3(15 - 3x) and sketch your solution.
7. How
many integer values of x satisfy 1/3(x – 1) < 5/7 < 1/5(x+4) ?
8. How
many positive integers p satisfy -1 < √p - √100 < 1?
9. If -2 < x < 3 then determine a and b in a < 2x + 3 < b.
10. What
values of x satisfy the inequality -3 < 5 - 2/x < 3? Sketch your solution.
11. Solve
2 - 1/x < 3 and sketch your solution.
12. Solve
2/x + 3 ≥ 4 and sketch your solution.
13. The
front wheel of Georgina's bicycle has a diameter of 0.75 metres. She cycled for
6 minutes at a speed of 24 kilometres per hour. How many complete rotations did
the wheel made during this time?
14. A
computer software retailer has 1200 copies of a new software package to sell. From
past experience, she knows that:
- Half of them will sell right away at the original price she sets,
- Two-thirds of the remainder will sell later when the price is reduced by 40%, and
- The remaining copies will sell in a clearance sale at 75% off the original price.
In order
to make a reasonable profit, the total sales revenue must be greater than or
equal to $72 000. To the nearest cent, what is the smallest original price she
should set?
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