Question

Solve for y in terms of xSolve for y:2/3x -1 = 2 (y+7)

Answer 1

Given the following equation:

`(2)/(3)x-1=2(y+7)`

You can solve for "y" in term of "x" applying the following steps:

1. You must apply the Distributive property, which states that

`\begin{gathered} a(b+c)=ab+ac \\ a(b-c)=ab-ac \end{gathered}`

Then:

`\begin{gathered} (2)/(3)x-1=(2)(y)+(2)(7) \\ \\ (2)/(3)x-1=2y+14 \end{gathered}`

2. Now you can apply the the Substraction property of equality by subtracting 14 from both sides of the equation:

`\begin{gathered} (2)/(3)x-1-(14)=2y+14-(14) \\ \\ (2)/(3)x-15=2y \end{gathered}`

3. Apply the Division property fo equality by dividing both sides of the equation by 2:

`\begin{gathered} (2)/(3\cdot2)x-(15)/(2)=(2y)/(2) \\ \\ (2)/(6)x-(15)/(2)=y \\ \\ (1)/(3)x-(15)/(2)=y \end{gathered}`

The answer is:

`y=(1)/(3)x-(15)/(2)`