Question

1/4(x+2)-1/3(x-1)=1/2(x+1). Solve equation and check solution.

Answer 1

Okay, here we have this:

`\begin{gathered} 1/4\mleft(x+2\mright)-1/3\mleft(x-1\mright)=1/2\mleft(x+1\mright) \\ (x+2)/(4)-(x-1)/(3)=(1)/(2)x+(1)/(2) \\ (\left(x+2\right)\cdot\:3)/(12)-(\left(x-1\right)\cdot\:4)/(12)=(1)/(2)x+(1)/(2) \\ (\left(x+2\right)\cdot\:3-\left(x-1\right)\cdot\:4)/(12)=(1)/(2)x+(1)/(2) \\ (-x+10)/(12)=(1)/(2)x+(1)/(2) \\ -(x)/(12)+(10)/(12)=(1)/(2)x+(1)/(2) \\ -(x)/(12)+(5)/(6)=(1)/(2)x+(1)/(2) \\ -(x)/(12)=-(1)/(3)+(1)/(2)x \\ -(7x)/(12)=-(1)/(3) \\ -7x=-4 \\ x=(4)/(7) \end{gathered}`

Now, let's check the solution:

`\begin{gathered} 1/4\mleft(x+2\mright)-1/3\mleft(x-1\mright)=1/2\mleft(x+1\mright) \\ 1/4\mleft((4)/(7)+2\mright)-1/3\mleft((4)/(7)-1\mright)=1/2\mleft((4)/(7)+1\mright) \\ (1)/(4)((18)/(7))-(1)/(3)(-(3)/(7))=(1)/(2)((11)/(7)) \\ (9)/(14)+(1)/(7)=(11)/(14) \\ (11)/(14)=(11)/(14) \end{gathered}`

Since the sides are equal, the result (x=4/7) is true.