Solve the following equations:

Q1.   4x-9=2x+7

Answer:

4x-9=2x+7

or 4x-2x=7+9

or 2x=16

or x=8

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Q2.  5x+18=11-2x

Answer:

5x+18=11-2x

or 5x+2x=11-18

or 7x=-7

or x=-1

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Q3.  21-3(x-7)=x+20

Answer:

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

or 21-3x+21=x+20

or 21+21-20=4x

or 22=4x

or x=5.4

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Q4.  3(x-7)-2(3x-4)=(2-5x)

Answer:

3(x-7)-2(3x-4)=(2-5x)  

or 3x-21-6x+8=2-5x

or -3x-13=2-5x

or 2x=15

or x=7.5

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Q5.  3(x-5)-16x=12-2(x-3)

Answer:

3(x-5)-16x=12-2(x-3)  

or 3x-15-16x=12-2x+6

or -13x-15=18-2x

or 11x=-33

or x= -3

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Q6.   \frac{3x}{4}-\frac{(x-4)}{3}=\frac{5}{3}

Answer:

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

or  \frac{9x-4(x-4)}{12}=\frac{5}{3}

or 27x-12(x-4)=60

or 27x-12x+48=60

or 15x=12

or x=\frac{4}{5}

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Q7.   \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

or 10(4x+1)+15(2x-1)-6(3x-7)=180 m25x

or 40x+10+30x-15-18x+42=180 

or 52x+37=180 \ or\  x=\frac{11}{4}

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Q8.   \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}

or 6(x+5)-4(x+1)=9(x+3) 

or 6x+30-4x-4=9x+27 

or 2x+26=9x+27 

or 7x=-1 

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

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Q9.  \frac{2-9x}{17-4x}=\frac{4}{5}

Answer:

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

or 5(2-9x)=4(17-4x) 

or 10-45x=68-16x 

or 29x=-58 

or x=-2 

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Q10.   \frac{2x-3}{3x-1}=\frac{2x+3}{3x+4}

Answer:

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

or (2x-3)(3x+4)=(3x-1)(2x+3) 

or 6x^2-9x+8x-12=6x^2-2x+9x-3 

or -x-12=7x-3 

or 8x=-9 

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

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Q11.   \frac{2-9x}{16+5x}=0

Answer:

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

or 2-9x=0 

or x=\frac{2}{9}

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Q12.    \frac{0.5x+4}{1.2x+6}=\frac{5}{3}

Answer:

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

or 3(0.5x+4)=5(1.2x+6) 

or 1.5x+12=6x+30 

or 4.5x=-18 

or x=-4 

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Q13.   \frac{3}{2x-1}+\frac{4}{2x+1}=\frac{7}{2x}

Answer:

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

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

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

or 12x^2+6x+16x^2-8x=28x^2-7 

or -2x=-7 

or x=\frac{7}{2}

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Q14.   \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}  

or  \frac{x-5}{x-2}=\frac{x+5}{x-1}

or (x-5)(x-1)=(x-2)(x+5) 

or x^2-5x-x+5=x^2-2x+5x-10 

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

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Q15.  (x+3)(x-3)-x(x+5)=6 

m26xAnswer:

(x+3)(x-3)-x(x+5)=6 

or x^2-9-x^2-5x=6 

or -9-5x=6 

or 5x=-15

or x=-3

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Q16. x(2x+3)-2x(x-5)=26

Answer:

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

or 2x^2+3x-2x^2+10x=26

or 13x=26

or x=2

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Q17.   \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

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

or 10x+60-25x+20+8x-24=0

or 7x=56

or x=8

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Q18.   \frac{3}{4}(7x-1)-(2x-\frac{1-x}{2})=x+\frac{3}{2}

Answer:

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

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

or 21x-3-8x+2-2x=4x+6

or 11x-1=4x+6

or 7x=7

or x=1

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