Solve the following equations:

Question 1:  4x-9=2x+7

Answer:

4x-9=2x+7

\Rightarrow 4x-2x=7+9

\Rightarrow 2x=16

\Rightarrow x=8

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Question 2: 5x+18=11-2x

Answer:

5x+18=11-2x

\Rightarrow 5x+2x=11-18

\Rightarrow 7x=-7

\Rightarrow x=-1

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Question 3: 21-3(x-7)=x+20

Answer:

21-3(x-7)=x+20

\Rightarrow 21-3x+21=x+20

\Rightarrow 21+21-20=4x

\Rightarrow 22=4x

\Rightarrow x=5.4

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Question 4: 3(x-7)-2(3x-4)=(2-5x)

Answer:

3(x-7)-2(3x-4)=(2-5x) 

\Rightarrow 3x-21-6x+8=2-5x

\Rightarrow -3x-13=2-5x

\Rightarrow 2x=15

\Rightarrow x=7.5

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Question 5: 3(x-5)-16x=12-2(x-3)

Answer:

3(x-5)-16x=12-2(x-3)

\Rightarrow 3x-15-16x=12-2x+6

\Rightarrow -13x-15=18-2x

\Rightarrow 11x=-33

\Rightarrow x= -3

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Question 6:  \frac{3x}{4} - \frac{(x-4)}{3} = \frac{5}{3}

Answer:

\frac{3x}{4} - \frac{(x-4)}{3} = \frac{5}{3}

\Rightarrow \frac{9x-4(x-4)}{12} = \frac{5}{3}

\Rightarrow 27x-12(x-4)=60

\Rightarrow 27x-12x+48=60

\Rightarrow 15x=12

\Rightarrow x= \frac{4}{5}

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Question 7:  \frac{(4x+1)}{3} + \frac{(2x-1)}{2} - \frac{(3x-7)}{5} =6

Answer:

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

\Rightarrow 10(4x+1)+15(2x-1)-6(3x-7)=180

\Rightarrow 40x+10+30x-15-18x+42=180

\Rightarrow 52x+37=180 \ or\ x= \frac{11}{4}

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Question 8: \frac{(x+5)}{6} - \frac{(x+1)}{9} = \frac{(x+3)}{4}

Answer:

\frac{(x+5)}{6} - \frac{(x+1)}{9} = \frac{(x+3)}{4}

\Rightarrow 6(x+5)-4(x+1)=9(x+3)

\Rightarrow 6x+30-4x-4=9x+27

\Rightarrow 2x+26=9x+27

\Rightarrow 7x=-1

\Rightarrow x=- \frac{1}{7}

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Question 9: \frac{2-9x}{17-4x}=\frac{4}{5}

Answer:

\frac{2-9x}{17-4x}=\frac{4}{5}

\Rightarrow 5(2-9x)=4(17-4x)

\Rightarrow 10-45x=68-16x

\Rightarrow 29x=-58

\Rightarrow x=-2

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Question 10:  \frac{2x-3}{3x-1} = \frac{2x+3}{3x+4}

Answer:

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

\Rightarrow (2x-3)(3x+4)=(3x-1)(2x+3)

\Rightarrow 6x^2-9x+8x-12=6x^2-2x+9x-3

\Rightarrow -x-12=7x-3

\Rightarrow 8x=-9

\Rightarrow x=- \frac{9}{8}

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Question 11:  \frac{2-9x}{16+5x} =0

Answer:

\frac{2-9x}{16+5x} =0

\Rightarrow 2-9x=0

\Rightarrow x= \frac{2}{9}

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Question 12:  \frac{0.5x+4}{1.2x+6} = \frac{5}{3}

Answer:

\frac{0.5x+4}{1.2x+6} = \frac{5}{3}

\Rightarrow 3(0.5x+4)=5(1.2x+6)

\Rightarrow 1.5x+12=6x+30

\Rightarrow 4.5x=-18

\Rightarrow x=-4

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Question 13:  \frac{3}{2x-1} + frac{4}{2x+1} = \frac{7}{2x}

Answer:

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

\Rightarrow \frac{3(2x+1)+4(2x-1)}{(2x-1)(2x+1)} = \frac{7}{2x}

\Rightarrow \frac{6x+3+8x-4}{4x^2-1} = \frac{7}{2x}

\Rightarrow 12x^2+6x+16x^2-8x=28x^2-7

\Rightarrow -2x=-7

\Rightarrow x= \frac{7}{2}

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Question 14:  \frac{3}{x-2} - \frac{2}{x-3} = \frac{4}{x-3} - \frac{3}{x-1}

Answer:

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

\Rightarrow \frac{x-5}{x-2} = \frac{x+5}{x-1}

\Rightarrow (x-5)(x-1)=(x-2)(x+5)

\Rightarrow x^2-5x-x+5=x^2-2x+5x-10

\Rightarrow -6x+5=3x-10 \ or\ x=\frac{15}{9}=\frac{5}{3}

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Question 15: (x+3)(x-3)-x(x+5)=6

Answer:

(x+3)(x-3)-x(x+5)=6

\Rightarrow x^2-9-x^2-5x=6

\Rightarrow -9-5x=6

\Rightarrow 5x=-15

\Rightarrow x=-3

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Question 16: x(2x+3)-2x(x-5)=26

Answer:

x(2x+3)-2x(x-5)=26

\Rightarrow 2x^2+3x-2x^2+10x=26

\Rightarrow 13x=26

\Rightarrow x=2

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Question 17:  \frac{x+6}{4} - \frac{5x-4}{8} + \frac{x-3}{5} =0

Answer:

\frac{x+6}{4} - \frac{5x-4}{8} + \frac{x-3}{5} =0

\Rightarrow 10(x+6)-5(5x-4)+8(x-3)=0

\Rightarrow 10x+60-25x+20+8x-24=0

\Rightarrow 7x=56

\Rightarrow x=8

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Question 18:  \frac{3}{4} (7x-1)- \Big( 2x- \frac{1-x}{2} \Big)=x+ \frac{3}{2}

Answer:

\frac{3}{4} (7x-1)- \Big( 2x- \frac{1-x}{2} \Big)=x+ \frac{3}{2}

\Rightarrow 3(7x-1)-(8x-2+2x)=4x+6

\Rightarrow 21x-3-8x+2-2x=4x+6

\Rightarrow 11x-1=4x+6

\Rightarrow 7x=7

\Rightarrow x=1