Let’s practice rearranging equations so that one variable is isolated.
Solve for [latex]x[/latex]:
[latex]2(-6x - 8y) = -9x[/latex]
Step 1: Distribute the 2
[latex]-12x - 16y = -9x[/latex]
Step 2: Move all [latex]x[/latex]-terms to one side
[latex]-12x + 9x = 16y[/latex]
Step 3: Combine like terms and divide
[latex]-3x = 16y \quad\Rightarrow\quad x = -\tfrac{16}{3}y[/latex]
Solve for [latex]x[/latex]:
[latex]y = x^2 + 4[/latex]
Step 1: Subtract 4 [latex]y - 4 = x^2[/latex] Step 2: Take the square root of both sides [latex]x = \pm \sqrt{y - 4}[/latex]
Solve for [latex]x[/latex]:
[latex]y = \dfrac{4}{9 - x}[/latex]
Step 1: Multiply both sides by [latex](9 - x)[/latex]
[latex]y(9 - x) = 4[/latex]
Step 2: Expand and rearrange
[latex]9y - xy = 4[/latex]
Step 3: Move terms with [latex]x[/latex] together
[latex]-xy = 4 - 9y[/latex]
Step 4: Divide by [latex]-y[/latex]
[latex]x = \dfrac{9y - 4}{y}[/latex]