Question

Solve each of the six equations. The, pair the equations together that have the same solution for x

Answer 1

For the first equation

`\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} \\ (4x)/(4)=(68)/(4) \\ x=17 \end{gathered}`

For the second equation

`\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} \\ (-3)/(3)=(3x)/(3) \\ -1=x \end{gathered}`

For the third equation

`\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} \\ (1.75x)/(1.75)=(29.75)/(1.75) \\ x=17 \end{gathered}`

For the fourth equation

`\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 \\ (-9x)/(-9)=(9)/(-9) \\ x=-1 \end{gathered}`

For the fifth equation

`\begin{gathered} (1)/(4)x+18=(3)/(4)(2x+5) \\ \text{ Apply distributive property} \\ (1)/(4)x+18=(6)/(4)x+(15)/(4) \\ \text{ Subtract }(6)/(4)x\text{from both sides of the equation} \\ (1)/(4)x+18-(6)/(4)x=(6)/(4)x+(15)/(4)-(6)/(4)x \\ (-5)/(4)x+18=(15)/(4) \\ \text{ Subtract 18 from both sides of the equation} \\ (-5)/(4)x+18-18=(15)/(4)-18 \\ (-5)/(4)x=(-57)/(4) \\ \text{ Multiplied by }(-4)/(5)\text{ on both sides of the equation} \\ (-5)/(4)x\cdot\text{ }(-4)/(5)=(-57)/(4)\cdot\text{ }(-4)/(5) \\ x=(57)/(5) \\ \text{ or} \\ x=11.4 \end{gathered}`

For the sixth equation

`\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 \\ (6x)/(6)=(68.4)/(6) \\ x=11.4 \end{gathered}`

Finally, matching equations that have the same solution for x you have

`\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 \\ (1)/(4)x+18=(3)/(4)(2x+5)\leftrightarrow3(2x-14.5)=24.9 \end{gathered}`