Question

2√(4 - 8y) = 12

Explanation:

Step1: Isolate the square root term

Divide both sides of the equation \(2\sqrt{4 - 8y}=12\) by 2.
\(\frac{2\sqrt{4 - 8y}}{2}=\frac{12}{2}\)
Simplify to get \(\sqrt{4 - 8y}=6\).

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{4 - 8y}=6\) to eliminate the square root.
\((\sqrt{4 - 8y})^2 = 6^2\)
Which simplifies to \(4 - 8y = 36\).

Step3: Solve for y

Subtract 4 from both sides: \(4 - 8y - 4 = 36 - 4\)
Simplify to \(-8y = 32\).
Then divide both sides by -8: \(\frac{-8y}{-8}=\frac{32}{-8}\)
So \(y = - 4\).

Step4: Check the solution

Substitute \(y = - 4\) back into the original equation \(2\sqrt{4 - 8y}\):
First, calculate the expression inside the square root: \(4-8\times(-4)=4 + 32 = 36\).
Then take the square root: \(\sqrt{36}=6\).
Multiply by 2: \(2\times6 = 12\), which matches the right - hand side of the original equation.

Answer:

\(y=-4\)