HomeworkAlgebraic Fractions, Equations and Inequalities

1. Simplify the following.

(a)

(b)

(c)

(d)

(e)

(f)

2. Simplify the following.(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

3. Simplify the following.(a)

(b)

(c)

(d)

(e)

(f)

4. Solve the following equations.(a) 5m + 6 = 26(b)

(c) 3x 17 = 4x(d) 7a = 14a 56

(e) 4 + 4m = 9m 11

(f)

5. Solve the following equations.(a) 3(5 + 3c) = 2(c 3)(b) 5(2x 16) = 4(1 x)(c)

(d) 3.2 3.5x = 9.6 4x(e)

(f) 2(x + 5) 4(3 x) 2 = 0(g) 3(2x + 1) 4(x 4) = 5 2(x 1)

6. Solve the following equations.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

7. Patrick is twice as old as Larry. Junxiangs age is half of Larrys age. The sum of their ages is 91. Find Junxiangs age.8. Jimmy saved $(3x + 25). Johnny saved $(5x 120). If the amount Johnny saved was $15 more than the amount Jimmy saved, find the amount that Johnny saved.

9. The sum of three consecutive positive numbers is 459. Find the greatest number.10. The sum of three consecutive odd numbers is 345. What are the three numbers?11. The breadth of a rectangle is 9 cm shorter than its length. If its perimeter is 150 cm, find its area.12. Julian and Irene had the same number of marbles. If Julian gave 72 marbles to Irene, Irene would have three times as many marbles as Julian. How many marbles did Irene have at first?13. The figure below shows a parallelogram. Find the value of x and of y.

14. Solve the following inequalities.(a) 3x 9(b) 8p > 72(c)

(d) 2b 5

(e) 7x > 34(f)

(g)

(h) 2k 3 < 5

15. Jiehua has a piece of paper with an area of 500 cm2. 30 cm2 of paper is needed to fold a paper aeroplane. Find the maximum number of paper aeroplanes he can fold using the piece of paper.16. During a fund raising event, $30 will be donated to charity for every fund raising ticket sold. Find the minimum number of tickets that have to be sold in order to raise at least $100000 for the donation to charity.

17. Abdul has $200. He can buy some watermelons at $4 each and 3 durians at $15 each. Find the maximum number of watermelons that he can buy.18. Mandy has a mass of x kg. Her mother has a mass of (2x 15) kg. Her fathers mass is greater than the total mass of Mandy and her mother. Given that x is a whole number and her fathers mass is 89 kg, find her mothers greatest possible mass.

End of Homework(4y 7) cm

2x cm

(5 x) cm

(x + y) cm

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