For the first equation
[tex]\begin{gathered} -4(x+5)+8x=48 \\ \text{ Appy distributive property} \\ -4x-20+8x=48 \\ \text{ Add like terms} \\ -20+4x=48 \\ \text{ Add 20 to both sides of the equation} \\ -20+4x+20=48+20 \\ 4x=68 \\ \text{ Divide to both sides of the equation by 4} \\ \frac{4x}{4}=\frac{68}{4} \\ x=17 \end{gathered}[/tex]For the second equation
[tex]\begin{gathered} -(2x-3)+4=-5x+2(3x+5) \\ \text{ Apply distributive property} \\ -2x+3+4=-5x+6x+10 \\ \text{ Add like terms} \\ -2x+7=x+10 \\ \text{ Add 2x to both sides of the equation} \\ -2x+7+2x=x+10+2x \\ 7=3x+10 \\ \text{ Subtract 10 from both sides of the equation} \\ 7-10=3x+10-10 \\ -3=3x \\ \text{ Divide both sides of the equation by 3} \\ \frac{-3}{3}=\frac{3x}{3} \\ -1=x \end{gathered}[/tex]For the third equation
[tex]\begin{gathered} 0.89x-8.75=21-0.86x \\ \text{ Add 8.75 to both sides of the equation} \\ 0.89x-8.75+8.75=21-0.86x+8.75 \\ 0.89x=29.75-0.86x \\ \text{ Subtract 0.86x from both sides of the equation} \\ 0.89x+0.86x=29.75-0.86x+0.86x \\ 1.75x=29.75 \\ \text{ Divide both sides of the equation by 1.75} \\ \frac{1.75x}{1.75}=\frac{29.75}{1.75} \\ x=17 \end{gathered}[/tex]For the fourth equation
[tex]\begin{gathered} 5(x-3)+8=14x+2 \\ \text{ Apply distributive property} \\ 5x-15+8=14x+2 \\ \text{ Add like terms} \\ 5x-7=14x+2 \\ \text{ Add 7 to both sides of the equation} \\ 5x-7+7=14x+2+7 \\ 5x=14x+9 \\ \text{ Subtract 14x from both sides of the equation} \\ 5x-14x=14x+9-14x \\ -9x=9 \\ \text{ Divide both sides of the equation by }-9 \\ \frac{-9x}{-9}=\frac{9}{-9} \\ x=-1 \end{gathered}[/tex]For the fifth equation
[tex]\begin{gathered} \frac{1}{4}x+18=\frac{3}{4}(2x+5) \\ \text{ Apply distributive property} \\ \frac{1}{4}x+18=\frac{6}{4}x+\frac{15}{4} \\ \text{ Subtract }\frac{6}{4}x\text{from both sides of the equation} \\ \frac{1}{4}x+18-\frac{6}{4}x=\frac{6}{4}x+\frac{15}{4}-\frac{6}{4}x \\ \frac{-5}{4}x+18=\frac{15}{4} \\ \text{ Subtract 18 from both sides of the equation} \\ \frac{-5}{4}x+18-18=\frac{15}{4}-18 \\ \frac{-5}{4}x=\frac{-57}{4} \\ \text{ Multiplied by }\frac{-4}{5}\text{ on both sides of the equation} \\ \frac{-5}{4}x\cdot\text{ }\frac{-4}{5}=\frac{-57}{4}\cdot\text{ }\frac{-4}{5} \\ x=\frac{57}{5} \\ \text{ or} \\ x=11.4 \end{gathered}[/tex]For the sixth equation
[tex]\begin{gathered} 3(2x-14.5)=24.9 \\ \text{ Apply distributive property} \\ 6x-43.5=24.9 \\ \text{ Add 43.5 to both sides of the equation} \\ 6x-43.5+43.5=24.9+43.5 \\ 6x=68.4 \\ \text{ Divide both sides of the equation by }6 \\ \frac{6x}{6}=\frac{68.4}{6} \\ x=11.4 \end{gathered}[/tex]Finally, matching equations that have the same solution for x you have
[tex]\begin{gathered} -4(x+5)+8x=48\leftrightarrow0.89x-8.75=21-0.86x \\ -(2x-3)+4=-5x+2(3x+5)\leftrightarrow5(x-3)+8=14x+2 \\ \frac{1}{4}x+18=\frac{3}{4}(2x+5)\leftrightarrow3(2x-14.5)=24.9 \end{gathered}[/tex]