Solve the following equations:

Question 1:  $4x-9=2x+7$

$4x-9=2x+7$

$\Rightarrow$ $4x-2x=7+9$

$\Rightarrow$ $2x=16$

$\Rightarrow$ $x=8$

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

$5x+18=11-2x$

$\Rightarrow$ $5x+2x=11-18$

$\Rightarrow$ $7x=-7$

$\Rightarrow$ $x=-1$

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

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

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

$\Rightarrow$ $21+21-20=4x$

$\Rightarrow$ $22=4x$

$\Rightarrow$ $x=5.4$

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

$3(x-7)-2(3x-4)=(2-5x)$

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

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

$\Rightarrow$ $2x=15$

$\Rightarrow$ $x=7.5$

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

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

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

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

$\Rightarrow$ $11x=-33$

$\Rightarrow$ $x= -3$

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

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

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

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

$\Rightarrow$ $27x-12x+48=60$

$\Rightarrow$ $15x=12$

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

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

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

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

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

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

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

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

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

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

$\Rightarrow$ $2x+26=9x+27$

$\Rightarrow$ $7x=-1$

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

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

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

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

$\Rightarrow$ $10-45x=68-16x$

$\Rightarrow$ $29x=-58$

$\Rightarrow$ $x=-2$

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

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

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

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

$\Rightarrow$ $-x-12=7x-3$

$\Rightarrow$ $8x=-9$

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

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Question 11:  $\frac{2-9x}{16+5x}$ $=0$

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

$\Rightarrow$ $2-9x=0$

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

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

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

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

$\Rightarrow$ $1.5x+12=6x+30$

$\Rightarrow$ $4.5x=-18$

$\Rightarrow$ $x=-4$

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

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

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

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

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

$\Rightarrow$ $-2x=-7$

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

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

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

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

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

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

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

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

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

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

$\Rightarrow$ $-9-5x=6$

$\Rightarrow$ $5x=-15$

$\Rightarrow$ $x=-3$

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

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

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

$\Rightarrow$ $13x=26$

$\Rightarrow$ $x=2$

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

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

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

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

$\Rightarrow$ $7x=56$

$\Rightarrow$ $x=8$

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

$\frac{3}{4}$ $(7x-1)- \Big( 2x-$ $\frac{1-x}{2}$ $\Big)=x+$ $\frac{3}{2}$
$\Rightarrow$ $3(7x-1)-(8x-2+2x)=4x+6$
$\Rightarrow$ $21x-3-8x+2-2x=4x+6$
$\Rightarrow$ $11x-1=4x+6$
$\Rightarrow$ $7x=7$
$\Rightarrow$ $x=1$