Question

Solve 2(x-6)+7x = 5-3(x-2)

Answer 1

`2(x-6)+7x=5-3(x-2)`

To solve x, let's eliminate the parenthesis first by multiplying 2 and -3 to it.

`2x-12+7x=5-3x+6`

Next, let's combine all like terms on either side. We will move -3x to the left side of the equation and -12 to the right side of the equation. Note that when a term crosses the equal symbol, the sign reverses. From -3x to +3x and from -12 to +12.

`2x+7x+3x=5+6+12`

Next, add the terms on both sides.

`12x=23`

Lastly, divide both sides by 12 to isolate x.

`\begin{gathered} (12x)/(12)=(23)/(12) \\ x=(23)/(12) \end{gathered}`

The value of x is 23/12.

Let's check if this is right by substituting the value of x to the equation.

`\begin{gathered} 2((23)/(12)-6)+7((23)/(12))=5-3((23)/(12)-2) \\ 2(-(49)/(12))+(161)/(12)=5-3(-(1)/(12)) \\ -(98)/(12)+(161)/(12)=5+(3)/(12) \\ (63)/(12)=(63)/(12) \\ (21)/(4)=(21)/(4) \end{gathered}`

Since we got the same 21/4 on both sides of the equation, our x value 23/12 is correct.