# SOLVING DIFFICULT EQUATIONS WORKSHEET

Problem 1 :

2x + 3 = 16 - (2x - 3)

Problem 2 :

5(x - 3) - 7(6 - x) = 24 - 3(8 - x) - 3

Problem 3 :

8(x - 1) + 17(x - 3) = 4(4x - 9) + 4

Problem 4 :

15(x - 1) + 4(x + 3) = 2(7 + x)

Problem 5 :

5x - (4x - 7)(3x - 5) = 6 - 3(4x - 9)(x - 1)

Problem 6 :

Problem 7 :

5x - 6(x - 5) = 2(x + 5) + 5(x - 4)

Problem 8 :

Problem 9 :

Problem 10 :

2x + 3 = 16 - (2x - 3)

2x + 3 = 16 - 2x + 3

2x + 3 = -2x + 19

4x + 3 = 19

4x = 16

x = 4

5(x - 3) - 7(6 - x) = 24 - 3(8 - x) - 3

5x - 15 - 42 + 7x = 24 - 24 + 3x - 3

12x - 57 = 3x - 3

9x - 57 = -3

9x = 54

x = 6

8(x - 1) + 17(x - 3) = 4(4x - 9) + 4

8x - 8 + 17x - 51 = 16x - 36 + 4

25x - 59 = 16x - 32

9x - 59 = -32

9x = 27

x = 3

15(x - 1) + 4(x + 3) = 2(7 + x)

15x - 15 + 4x + 12 = 14 + 2x

19x - 3 = 14 + 2x

17x - 3 = 14

17x = 17

x = 1

5x - (4x - 7)(3x - 5) = 6 - 3(4x - 9)(x - 1)

5x - (12x2- 20x - 21x + 35) = 6 - 3(4x2- 4x - 9x + 9)

5x - (12x2- 41x + 35) = 6 - 3(4x2- 13x + 9)

5x - 12x+ 41x - 35 = 6 - 12x+ 39x - 27

-12x+ 46x - 35 = -12x+ 39x - 21

46x - 35 = 39x - 21

7x - 35 = -21

7x = 14

x = 2

Least common multiple of the denominators 4 and 5 is 20. Multiply both sides of the equation by 20 to get rid of the denominators and solve for x..

16x - 35 = 4x + 5x

16x - 35 = 9x

7x - 35 = 0

7x = 35

x = 5

5x - 6(x - 5) = 2(x + 5) + 5(x - 4)

5x - 6x + 30 = 2x + 10 + 5x - 20

-x + 30 = 7x - 10

-8x + 30 = -10

-8x = -40

x = 5

9(x - 2) + 2(x + 10) = 90

9x - 18 + 2x + 20 = 90

11x + 2 = 90

11x = 88

x = 8

52(x + 2) = 455 + 5(5x)

52x + 104 = 455 + 25x

27x + 104 = 455

27x = 351

x = 13

6(x + 35) - 4(x + 7) = 9(x + 21)

6x + 210 - 4x - 28 = 9x + 189

2x + 182 = 9x + 189

-7x + 182 = 189

-7x = 7

x = -1

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