Question

Solve for the value of x.-2/3(x+12)+2/3x=-5/4x+2

Answer 1

`-(2)/(3)(x+12)+(2)/(3)x=-(5)/(4)x+2`

To solve for the value of x, let's simplify the equation by eliminating the parenthesis first applying the distributative property.

`-(2)/(3)x-8+(2)/(3)x=-(5)/(4)x+2`

The next step is to join similar terms on each side. Let's transfer -5/4x to the other side and -8 to the right side. In doing so, the signs will reverse as well. From positive to negative and vice versa.

`\begin{gathered} -(2)/(3)x+(2)/(3)x+(5)/(4)x=2+8 \\ (5)/(4)x=10 \end{gathered}`

The last step is to divide both sides of the equation by 5/4 to solve for x.

`\begin{gathered} ((5)/(4))/((5)/(4))x=(10)/((5)/(4)) \\ x=8 \end{gathered}`

Therefore, the value of x is 8.

To check if it is correct, we can substitute the x value in the original equation by 8 and see if both sides are indeed equal.

`\begin{gathered} -(2)/(3)(8+12)+(2)/(3)(8)=-(5)/(4)(8)+2 \\ -(2)/(3)(20)+(16)/(3)=-10+2 \\ -(40)/(4)+(16)/(3)=-8 \\ -(24)/(3)=-8 \\ -8=-8 \end{gathered}`

Indeed both sides are equal therefore, the value of x must be 8.