Question

Rewrite the equation so that \(y\) is a function of \(x .\) $$\frac{1}{3}(y+2)+3 x=7 x$$

Short answer

The given equation, when rewritten as a function of 'x', will be \(y = 12x - 2\).

Step-by-step solution

Simplification

This step involves simplification of the given equation. For this equation particular, we distribute the fraction \(\frac{1}{3}\) across \(y + 2\). This simplifies to \(\frac{1}{3}y + \frac{2}{3} + 3x = 7x\). Next, we can combine like terms by subtracting \(3x\) from both sides. This gives us \(\frac{1}{3}y + \frac{2}{3} = 4x\).

Isolate 'y'

In this step, we aim to have 'y' on one side of the equation alone. We can do this by subtracting \(\frac{2}{3}\) from both sides. This will give us \(\frac{1}{3}y = 4x - \frac{2}{3}\).

Solve for 'y'

To make 'y' the subject of the formula, we multiply through by 3. This results in \(y = 12x - 2\).