\displaystyle \textbf{Solve the following equations:}

\displaystyle \textbf{Question 1: }4x-9=2x+7
\displaystyle \text{Answer:}
\displaystyle 4x-9=2x+7
\displaystyle \Rightarrow 4x-2x=7+9
\displaystyle \Rightarrow 2x=16
\displaystyle \Rightarrow x=8
\displaystyle \\

\displaystyle \textbf{Question 2: }5x+18=11-2x
\displaystyle \text{Answer:}
\displaystyle 5x+18=11-2x
\displaystyle \Rightarrow 5x+2x=11-18
\displaystyle \Rightarrow 7x=-7
\displaystyle \Rightarrow x=-1
\displaystyle \\

\displaystyle \textbf{Question 3: }21-3(x-7)=x+20
\displaystyle \text{Answer:}
\displaystyle 21-3(x-7)=x+20
\displaystyle \Rightarrow 21-3x+21=x+20
\displaystyle \Rightarrow 42-3x=x+20
\displaystyle \Rightarrow 42-20=x+3x
\displaystyle \Rightarrow 22=4x
\displaystyle \Rightarrow x=\frac{22}{4}=\frac{11}{2}=5.5
\displaystyle \\

\displaystyle \textbf{Question 4: } 3(x-7)-2(3x-4)=2-5x
\displaystyle \text{Answer:}
\displaystyle 3(x-7)-2(3x-4)=2-5x
\displaystyle \Rightarrow 3x-21-6x+8=2-5x
\displaystyle \Rightarrow -3x-13=2-5x
\displaystyle \Rightarrow -3x+5x=2+13
\displaystyle \Rightarrow 2x=15
\displaystyle \Rightarrow x=\frac{15}{2}=7.5
\displaystyle \\

\displaystyle \textbf{Question 5: } 3(x-5)-16x=12-2(x-3)
\displaystyle \text{Answer:}
\displaystyle 3(x-5)-16x=12-2(x-3)
\displaystyle \Rightarrow 3x-15-16x=12-2x+6
\displaystyle \Rightarrow -13x-15=18-2x
\displaystyle \Rightarrow -13x+2x=18+15
\displaystyle \Rightarrow -11x=33
\displaystyle \Rightarrow x=-3
\displaystyle \\

\displaystyle \textbf{Question 6: } \frac{3x}{4}-\frac{x-4}{3}=\frac{5}{3}
\displaystyle \text{Answer:}
\displaystyle \frac{3x}{4}-\frac{x-4}{3}=\frac{5}{3}
\displaystyle \Rightarrow 12\left(\frac{3x}{4}\right) -12\left(\frac{x-4}{3}\right)=12\left(\frac{5}{3}\right)
\displaystyle \Rightarrow 9x-4(x-4)=20
\displaystyle \Rightarrow 9x-4x+16=20
\displaystyle \Rightarrow 5x=4
\displaystyle \Rightarrow x=\frac{4}{5}
\displaystyle \\

\displaystyle \textbf{Question 7: } \frac{4x+1}{3}+\frac{2x-1}{2}-\frac{3x-7}{5}=6
\displaystyle \text{Answer:}
\displaystyle \frac{4x+1}{3}+\frac{2x-1}{2}-\frac{3x-7}{5}=6
\displaystyle \Rightarrow 10(4x+1)+15(2x-1)-6(3x-7)=180
\displaystyle \Rightarrow 40x+10+30x-15-18x+42=180
\displaystyle \Rightarrow 52x+37=180
\displaystyle \Rightarrow 52x=143
\displaystyle \Rightarrow x=\frac{143}{52}=\frac{11}{4}
\displaystyle \\

\displaystyle \textbf{Question 8: } \frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}
\displaystyle \text{Answer:}
\displaystyle \frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}
\displaystyle \Rightarrow 6(x+5)-4(x+1)=9(x+3)
\displaystyle \Rightarrow 6x+30-4x-4=9x+27
\displaystyle \Rightarrow 2x+26=9x+27
\displaystyle \Rightarrow 2x-9x=27-26
\displaystyle \Rightarrow -7x=1
\displaystyle \Rightarrow x=-\frac{1}{7}
\displaystyle \\

\displaystyle \textbf{Question 9: } \frac{2-9x}{17-4x}=\frac{4}{5}
\displaystyle \text{Answer:}
\displaystyle \frac{2-9x}{17-4x}=\frac{4}{5}
\displaystyle \Rightarrow 5(2-9x)=4(17-4x)
\displaystyle \Rightarrow 10-45x=68-16x
\displaystyle \Rightarrow -45x+16x=68-10
\displaystyle \Rightarrow -29x=58
\displaystyle \Rightarrow x=-2
\displaystyle \\

\displaystyle \textbf{Question 10: } \frac{2x-3}{3x-1}=\frac{2x+3}{3x+4}
\displaystyle \text{Answer:}
\displaystyle \frac{2x-3}{3x-1}=\frac{2x+3}{3x+4}
\displaystyle \Rightarrow (2x-3)(3x+4)=(2x+3)(3x-1)
\displaystyle \Rightarrow 6x^2+8x-9x-12 =6x^2-2x+9x-3
\displaystyle \Rightarrow -x-12=7x-3
\displaystyle \Rightarrow -x-7x=-3+12
\displaystyle \Rightarrow -8x=9
\displaystyle \Rightarrow x=-\frac{9}{8}
\displaystyle \\

\displaystyle \textbf{Question 11: } \frac{2-9x}{16+5x}=0
\displaystyle \text{Answer:}
\displaystyle \frac{2-9x}{16+5x}=0
\displaystyle \Rightarrow 2-9x=0,\qquad 16+5x\ne0
\displaystyle \Rightarrow 9x=2
\displaystyle \Rightarrow x=\frac{2}{9}
\displaystyle \text{For }x=\frac{2}{9},\ 16+5x\ne0.
\displaystyle \therefore x=\frac{2}{9}\text{ is the solution.}
\displaystyle \\

\displaystyle \textbf{Question 12: } \frac{0.5x+4}{1.2x+6}=\frac{5}{3}
\displaystyle \text{Answer:}
\displaystyle \frac{0.5x+4}{1.2x+6}=\frac{5}{3}
\displaystyle \Rightarrow 3(0.5x+4)=5(1.2x+6)
\displaystyle \Rightarrow 1.5x+12=6x+30
\displaystyle \Rightarrow 1.5x-6x=30-12
\displaystyle \Rightarrow -4.5x=18
\displaystyle \Rightarrow x=-4
\displaystyle \\

\displaystyle \textbf{Question 13: } \frac{3}{2x-1}+\frac{4}{2x+1}=\frac{7}{2x}
\displaystyle \text{Answer:}
\displaystyle \frac{3}{2x-1}+\frac{4}{2x+1}=\frac{7}{2x}
\displaystyle \Rightarrow \frac{3(2x+1)+4(2x-1)}{(2x-1)(2x+1)}=\frac{7}{2x}
\displaystyle \Rightarrow \frac{6x+3+8x-4}{4x^2-1}=\frac{7}{2x}
\displaystyle \Rightarrow \frac{14x-1}{4x^2-1}=\frac{7}{2x}
\displaystyle \Rightarrow 2x(14x-1)=7(4x^2-1)
\displaystyle \Rightarrow 28x^2-2x=28x^2-7
\displaystyle \Rightarrow -2x=-7
\displaystyle \Rightarrow x=\frac{7}{2}
\displaystyle \\

\displaystyle \textbf{Question 14: } \frac{3}{x-2}-\frac{2}{x-3} =\frac{4}{x-3}-\frac{3}{x-1}
\displaystyle \text{Answer:}
\displaystyle \frac{3}{x-2}-\frac{2}{x-3} =\frac{4}{x-3}-\frac{3}{x-1}
\displaystyle \Rightarrow \frac{3(x-3)-2(x-2)}{(x-2)(x-3)} =\frac{4(x-1)-3(x-3)}{(x-3)(x-1)}
\displaystyle \Rightarrow \frac{x-5}{(x-2)(x-3)} =\frac{x+5}{(x-3)(x-1)}
\displaystyle \Rightarrow \frac{x-5}{x-2}=\frac{x+5}{x-1},\qquad x\ne3
\displaystyle \Rightarrow (x-5)(x-1)=(x+5)(x-2)
\displaystyle \Rightarrow x^2-6x+5=x^2+3x-10
\displaystyle \Rightarrow -6x+5=3x-10
\displaystyle \Rightarrow -9x=-15
\displaystyle \Rightarrow x=\frac{15}{9}=\frac{5}{3}
\displaystyle \\

\displaystyle \textbf{Question 15: } (x+3)(x-3)-x(x+5)=6
\displaystyle \text{Answer:}
\displaystyle (x+3)(x-3)-x(x+5)=6
\displaystyle \Rightarrow x^2-9-x^2-5x=6
\displaystyle \Rightarrow -9-5x=6
\displaystyle \Rightarrow -5x=15
\displaystyle \Rightarrow x=-3
\displaystyle \\

\displaystyle \textbf{Question 16: } x(2x+3)-2x(x-5)=26
\displaystyle \text{Answer:}
\displaystyle x(2x+3)-2x(x-5)=26
\displaystyle \Rightarrow 2x^2+3x-2x^2+10x=26
\displaystyle \Rightarrow 13x=26
\displaystyle \Rightarrow x=2
\displaystyle \\

\displaystyle \textbf{Question 17: } \frac{x+6}{4}-\frac{5x-4}{8}+\frac{x-3}{5}=0
\displaystyle \text{Answer:}
\displaystyle \frac{x+6}{4}-\frac{5x-4}{8}+\frac{x-3}{5}=0
\displaystyle \Rightarrow 10(x+6)-5(5x-4)+8(x-3)=0
\displaystyle \Rightarrow 10x+60-25x+20+8x-24=0
\displaystyle \Rightarrow -7x+56=0
\displaystyle \Rightarrow -7x=-56
\displaystyle \Rightarrow x=8
\displaystyle \\

\displaystyle \textbf{Question 18: } \frac{3}{4}(7x-1)-\left(2x-\frac{1-x}{2}\right) =x+\frac{3}{2}
\displaystyle \text{Answer:}
\displaystyle \frac{3}{4}(7x-1)-\left(2x-\frac{1-x}{2}\right) =x+\frac{3}{2}
\displaystyle \Rightarrow 3(7x-1)-4\left(2x-\frac{1-x}{2}\right)=4x+6
\displaystyle \Rightarrow 3(7x-1)-8x+2(1-x)=4x+6
\displaystyle \Rightarrow 21x-3-8x+2-2x=4x+6
\displaystyle \Rightarrow 11x-1=4x+6
\displaystyle \Rightarrow 7x=7
\displaystyle \Rightarrow x=1
\displaystyle \\

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