Solve the following equations:

Exercise 1

2x = 6

 

Exercise 2

2x -3 = 6 + x

 

Exercise 3

2 (2x - 3) = 6 + x

 

Exercise 4

\frac{x - 1}{6} - \frac{x - 3}{2} = -1

 

Exercise 5

\frac{3}{4} (2x + 4) = x + 19

 

Exercise 6

4 (x - 10) = -6 (2 - x) -6x

 

Exercise 7

2 (x + 1) - 3(x - 2) = x + 6

 

Exercise 8

\frac{x - 1}{4} - \frac{x - 5}{36} = \frac{x + 5}{9}

 

Exercise 9

\frac{3x + 1}{7} - \frac{2 - 4x}{3} = \frac{-5x - 4}{14} + \frac{7x}{6}

 

Exercise 10

\frac{5}{x - 7} = \frac{3}{x - 2}

 

Exercise 11

\frac{4}{x - 3} = \frac{5}{x - 2}

 

Exercise 12

6 (\frac{x + 1}{8} - \frac{2x - 3}{16}) = 3(\frac{3}{4}x - \frac{1}{4}) - \frac{3}{8} (3x - 2)

 

Exercise 13

2 - [-2 \cdot (x + 1) - \frac{x - 3}{2}] = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

 

Exercise 14

\frac{2}{3} [ x - (1 - \frac{x - 2}{3})] + 1 = x

 

Exercise 15

2 - [-2 \cdot (x + 1) - \frac{x - 3}{2}] = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

 

 

Solution of exercise 1

2x = 6

x = \frac{6}{2}

x = 3

 

Solution of exercise 2

2x - 3 = 6 + x

2x -x = 6 + 3

x = 9

 

Solution of exercise 3

2 (2x - 3) = 6 + x

4x - 6 = 6 + x

4x - x = 6 + 6

3x = 12

x = \frac{12}{3}

x = 4

 

Solution of exercise 4

\frac{x - 1}{6} - \frac{x - 3}{2} = -1

LCM (6, 2) = 6

x - 1 - 3 (x - 3) = -6

x - 1 - 3x + 9 = -6

x - 1 - 3x + 9 = -6

x - 3x = -6 - 9 + 1

-2x = -14

x = \frac{14}{2}

x = 7

 

 

Solution of exercise 5

\frac{3}{4} (2x + 4) = x + 19

\frac{6}{4}x + \frac{12}{4} = x + 19

\frac{3}{2}x + 3 = x + 19

3x + 6 = 2x + 38

3x - 2x = 38 - 6

x = 32

 

Solution of exercise 6

4 (x - 10) = -6 (2 - x) -6x

4x - 40 = -12 + 6x - 6x

4x - 6x + 6x = -12 + 40

4x = 28

x = 7

 

Solution of exercise 7

2 (x + 1) - 3(x - 2) = x + 6

2x + 2 - 3x + 6 = x + 6

2x - 3x - x = 6 -2 - 6

-2x = -2

x = 1

 

Solution of exercise 8

\frac{x - 1}{4} - \frac{x - 5}{36} = \frac{x + 5}{9}

LCM (4, 36, 9) = 36

9 (x - 1) - (x - 5) = 4 (x + 5)

9x - 9 - x + 5 = 4x + 20

9x - x - 4x = 20 + 9 - 5

4x = 24

x = 6

 

Solution of exercise 9

\frac{3x + 1}{7} - \frac{2 - 4x}{3} = \frac{-5x - 4}{14} + \frac{7x}{6}

LCM (7, 3, 14, 6) = 42

6(3x + 1) - 14 (2 - 4x) = 3 (-5x - 4) + 49x

18x + 6 - 28 + 56x = -15x - 12 + 49x

18x + 56x + 15x - 49x = -12 - 6 + 28

40x = 10

4x = 1

x = \frac{1}{4}

 

Solution of exercise 10

\frac{5}{x - 7} = \frac{3}{x - 2}

5 (x - 2) = 3 (x - 7)

5x - 10 = 3x - 21

5x - 3x = -21 + 10

2x = -11

x = -\frac{11}{2}

 

Solution of exercise 11

\frac{4}{x - 3} = \frac{5}{x - 2}

4 (x - 2) = 5 (x - 3)

4x - 8 = 5x - 15

-8 + 15 = 5x - 4x

x = 7

 

Solution of exercise 12

6 (\frac{x + 1}{8} - \frac{2x - 3}{16}) = 3 (\frac{3}{4}x - \frac{1}{4}) - \frac{3}{8}(3x - 2)

\frac{6(x +1)}{8} - \frac{6 (2x - 3)}{16} = \frac{9}{4}x - \frac{3}{4} - \frac{9}{8}x + \frac{6}{8}

\frac{6x + 6}{8} - \frac{12x - 18}{16} = \frac{9}{4}x - \frac{3}{4} - \frac{9}{8}x + \frac{6}{8}

LCM (8, 16, 4) = 16

2(6x + 6) - (12x - 18) = 36x - 12 - 28x + 12

12+ 18 = 36x - 18x

18x = 30

3x = 5

x = \frac{5}{3}

 

Solution of exercise 13

2 - [-2 \cdot (x + 1) - \frac{x - 3}{2}] = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

2 - (-2x - 2 - \frac{x - 3}{2}) = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

2 + 2x + 2 + \frac{x - 3}{2} = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

24 + 24x + 24 + 6 \cdot (x - 3) = 8x - (5x - 3) + 36x

24 + 24x + 24 + 6x - 18 = 8x - 5x + 3 + 36x

24x + 6x - 8x + 5x - 36x = 3 - 24 - 24 + 18

-9x = -27

x = 3

 

Solution of exercise 14

\frac{2}{3} [ x - (1 - \frac{x - 2}{3})] + 1 = x

\frac{2}{3} (x - 1 + \frac{x - 2}{3}) + 1 = x

\frac{2}{3}x - \frac{2}{3} + \frac{2x - 4}{9} + 1 = x

6x - 6 + 2x - 4 + 9 = 9x

-x = 1

x = -1

 

Solution of exercise 15

2 - [-2 \cdot (x + 1) - \frac{x - 3}{2}] = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

2 - (-2x - 2 - \frac{x - 3}{2}) = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

2 + 2x + 2 + \frac{x - 3}{2} = \frac{2x}{3} - \frac{5x - 3}{12} + 3x

24 + 24x + 24 + 6 \cdot (x - 3) = 8x - (5x - 3) + 36x

24 + 24 x + 24 + 6x - 18 = 8x - 5x + 3 + 36x

24x + 6x - 8x + 5x - 36x = 3 - 24 - 24 + 18

-9x = -27

x = 3

 

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.