Question

$\frac{1}{4}x + 12 = x - 6$

Explanation:

Step1: Eliminate fraction by multiplying all terms by 4.

Multiply each term in the equation \(\frac{1}{4}x + 12 = x - 6\) by 4 to get rid of the fraction. So we have \(4\times\frac{1}{4}x + 4\times12 = 4\times x - 4\times6\), which simplifies to \(x + 48 = 4x - 24\).

Step2: Move all x terms to one side and constants to the other.

Subtract \(x\) from both sides: \(x - x + 48 = 4x - x - 24\), which gives \(48 = 3x - 24\). Then add 24 to both sides: \(48 + 24 = 3x - 24 + 24\), so \(72 = 3x\).

Step3: Solve for x.

Divide both sides by 3: \(\frac{72}{3}=\frac{3x}{3}\), which gives \(x = 24\).

Answer:

\(x = 24\)