Question

Solve the equation. Explain or show your reasoning.1/2 x -7 = 1/3 (x-12)

Answer 1

You have to solve the following equation

`(1)/(2)x-7=(1)/(3)(x-12)`

To solve this equation means that you have to calculate it for x.

The first step is to solve the multiplication on the parentheses term, to do so you have to apply the distributive property of multiplication:

`\begin{gathered} (1)/(2)x-7=(1)/(3)\cdot x-(1)/(3)\cdot12 \\ (1)/(2)x-7=(1)/(3)x-4 \end{gathered}`

Then you have to pass the x-term to the left side of the equation and the constant to the right side by applying the opposite operation to both sides of the equal sign

`\begin{gathered} (1)/(2)x-(1)/(3)x-7=(1)/(3)x-(1)/(3)x-4 \\ (1)/(3)x-7=-4 \\ (1)/(3)x-7+7=-4+7 \\ (1)/(3)x=3 \end{gathered}`

Finally, as you can see the x term is multiplied by 1/3, to cancel this multiplication you have to divide both sides of the equation by 1/3 or what is the same, multiply it by the reciprocate fraction 3/1 or simply put 3

`\begin{gathered} ((1)/(3)\cdot3)x=3\cdot3 \\ x=9 \end{gathered}`

The value of x is 9