©teejay publishers homework for level f book ch 43 -equations/inequalities 43 equations.pdf ·...

©TeeJay Publishers Homework for Level F book Ch 43 -Equations/Inequalities

this is Chapter Forty Three page 67 EQUATIONS

Exercise 1

1. Copy each equation and solve it to find the value of x :-

(a) x + 9 = 15 (b) x + 11 = 11 (c) x – 8 = 4

(d) x – 18 = 0 (e) x – 60 = 20 (f) x + 8 = 3

(g) x + 19 = 0 (h) 3 + x = 5 (i) 22 + x = 1.

2. Copy each equation and solve it to find the value of the letter :-

(a) 2m = 26 (b) 7k = 0 (c) 4x = 2

(d) 8u = 12 (e) 8v = 18 (f) 15p = 10.

3. Find the value of x in the following equations (Show each step of working carefully).

(a) 4x + 1 = 21 (b) 3x + 5 = 29 (c) 9x – 3 = 15

(d) 7x – 6 = 29 (e) 6x – 12 = 0 (f) 5x – 1 = 44

(g) 9x – 20 = 34 (h) 3x + 42 = 87 (i) 2x – 7 = 32

(j) 9x + 9 = 0 (k) 2x – 19 = 0 (l) 3x + 5 = –7.

Exercise 2

1. Solve the following equations :-

(a) 5x + 3 = 3x + 5 (b) 8x + 9 = 7x + 17 (c) 7x – 1 = 3x + 15

(d) 5x – 3 = 2x + 18 (e) 12x – 5 = 8x + 7 (f) 10x – 1 = 8x + 6

(g) 6x + 4 = 3x + 4 (h) 9x – 1 = 4x + 34 (i) 7x – 8 = x + 1.

2. Solve for x :-

(a) 4x = 3x + 8 (b) 4x = x + 18 (c) 9x = 4x + 45

(d) 10x = 9x + 41 (e) 3x = x + 17 (f) 5x – 26 = 3x

(g) 7x – 48 = x (h) 3x + 17 = x (i) 10x – 30 = 6x.

Chapter 43 Equations & Inequations



3. Simon had 6 boxes of disks. Amy had only 1 box of disks but had 50 loose disks as well.

They discovered that they had exactly the same number of disks.

(a) Make up an equation to show this information. (let x be the number of disks in 1 box)

(b) Solve the equation to determine how many disks there are in each box.

4. A large group of friends decide to go to a football match.They fill 6 taxis and 4 of them also to walk to the match.

Afterwards, they have 4 taxis (full) to take them back. The remaining 16 friends walk home.

(a) Make up an equation to show this information. (let x be the number of people in 1 full taxi)

(b) Solve the equation to determine how many people a full taxi carried.

Exercise 31. Solve these equations by multiplying out the brackets first :-

(a) 2(x + 7) = 18 (b) 3(x + 4) = 30 (c) 5(x – 6) = 10

(d) 4(x + 9) = 48 (e) 6(x + 3) = 66 (f) 2(x + 5) = 18

(g) 9(x – 4) = 36 (h) 9(x + 1) = 9 (i) 2(x – 1) = 11

(j) 5(x – 7) = 0 (k) 3(x – 8) = 9 (l) 5(x + 7) = 20.

2. Solve these equations :-

(a) 2(4x + 3) = 14 (b) 5(2x – 1) = 45 (c) 3(6x – 1) = 33

(d) 2(7x + 4) = 50 (e) 3(2x – 8) = 0 (f) 4(5x – 8) = 88

(g) 2(3x – 1) = 4x + 14 (h) 5(2x + 1) = 7x + 14 (i) 3(1 + 2x) = 5x + 17

(j) 6(2x – 1) = 10x (k) 14(2x – 1) = 26x + 4 (l) 8(x + 3) = 7x.

3. Solve the equations :-

(a) 2(x + 5) – x – 4 = 7 (b) 4(x + 2) + 3x – 3 = 12

(c) 5(x + 2) – 3x = 18 (d) 3(x – 5) + 4x + 1 = 28

(e) 2x + 1 + 3(x – 6) = 23 (f) 8x + 2(x – 9) = 82

(g) 3(x – 3) + 2(x + 5) = 21 (h) 5(2x + 1) + 3(1 – 2x) = 20

(i) 5(2x + 1) – 2(x – 2) = 6x + 13 (j) 10(x + 3) – 6(x + 1) = 2x + 40.



Exercise 4

Solve each of these equations, by first of all multiplying every term by the l.c.m. of all the fractional denominators :–

1. 12

x – 3 = 1 2. 14

x + 7 = 10 3. 18

x – 5 = 0

4. 23

x – 1 = 9 5. 1 + 35

x = 13 6. 38

x + 4 = 4

7. 34

x – 12

= 7 8. 12

x + 13

= 4 9. 45

x – 14

= 0

10. 12

x – 5 = 14

11. 23

x – 1 = 16

12. 34

x – 1 = 15

13. 12

x + 1 = 13

x + 4 14. 34

x – 4 = 35

x – 1 15. 1 + 58

x = 14

x + 10.

Exercise 5

Multiply each term by the l.c.m. of the denominators to dispose of the fractions and solve :-

1.

€

x + 14

= 3 2.

€

x + 45

= 4

3.

€

x + 23

– 2 = 5 4. 8 –

€

x − 53

= 0

5. 23

(6x + 3) – 22 = 0 6. 34

(5x – 1) – 7 = 3 12

7. 58

(x + 3) – 12

x = 2 8. 25

(6x – 1) – 13

x = 12

9. 2 + 310

(2x + 6) = 13

x + 7 10. 23

(2x + 4) + 12

(x – 3) = 14

11.

€

x − 15

+

€

x + 23

= 1 12.

€

2x − 14

–

€

x + 63

= 0.



Exercise 6

1. Solve these inequalities, leaving your answers in the form x < 1, etc. :–

(a) x + 4 > 7 (b) x + 8 < 14 (c) x – 9 ≤ 20

(d) x + 6 ≥ 23 (e) x – 15 ≤ 15 (f) x – 61 ≥ 0

2. Solve each inequality, leaving your answers in the form x ≥ 7, etc. :–

(a) 5x < 25 (b) 4x > 28 (c) 3x < 39

(d) 9x ≥ 54 (e) 7x ≤ 98 (f) 100x > 1400

3. Solve the following inequalities :-

(a) 3x + 5 < 23 (b) 2x + 11 > 27 (c) 6x – 8 < 4

(d) 7x + 3 ≥ 52 (e) 10x – 9 ≤ 81 (f) 5x – 23 > 7

(g) 4x + 4 ≤ 4 (h) 3x – 2 < 25 (i) 2x + 5 ≤ 22

(j) 2(x + 5) < 16 (k) 4(x + 8) > 40 (l) 4(x – 1) ≥ 20

(m) 4(2x + 1) ≤ 84 (n) 2(6x – 4) > 4 (o) 5(x + 3) < 3x + 21

(p) 3(2x – 7) ≥ 5x + 19 (q) 2(8x + 1) < 3x + 2 (r) 7(2x – 1) ≤ 12x



Revision Exercise

1. Find the value of x in the following equations (Show each step of working carefully).

(a) x + 5 = 19 (b) x – 40 = 10 (c) 9x = 54

(d) 2x = 17 (e) 10x = 5 (f) 4x + 1 = 21

(g) 9x – 6 = 30 (h) 2x + 7 = 14 (i) 3x – 2 = –11

(j) 5x + 1 = 3x + 7 (k) 7x – 1 = 4x + 14 (l) 9x = 3x + 42

2. Don had 9 packets of toffos. He gave 2 packets to Emma, who also had 25 loose toffos.

They discovered that they then had exactly the same number of toffos.

(a) Make up an equation to show this information.

(let x be the number of toffos in 1 packet)

(b) Solve the equation to determine how many toffos there are in each packet.

3. Solve these equations :-

(a) 3(x + 5) = 36 (b) 8(x – 3) = 40

(c) 2(3x + 1) = 38 (d) 9(2x – 8) = 0

(e) 5(3x – 2) = 5x (f) 8(2x – 1) = 4x + 16

(g) 8(x + 2) – 6x = 21 (h) 5(2x – 1) + 3(1 + x) = 37

4. Multiply each term by the l.c.m. of the denominators to dispose of the fractions and solve :-

(a) 12

x – 5 = 4 (b) 12

x + 13

= 3

(c)

€

x + 25

– 2 = 0 (d)

€

x − 14

–

€

x + 110

= 1

5. Solve the following inequalities :-

(a) x + 8 > 11 (b) x – 12 ≤ 12 (c) x – 32 ≥ 0

(d) 4x < 64 (e) 2x + 18 > 24 (f) 3(2x + 1) ≤ 33

(g) 3(2x – 4) ≥ 5x + 17 (h) 2(3x + 1) < 4x – 2 (i) 6(2x – 4) ≤ 9x

©teejay publishers homework for level f book ch 43 -equations/inequalities 43 equations.pdf ·...

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