Question

solve for x.
2 - x = 2\left(3 - \frac{1}{4}x\
ight)
x = \square

Explanation:

Step1: Distribute the 2 on the right

Multiply 2 by each term inside the parentheses: \(2 - x = 2\times3 - 2\times\frac{1}{4}x\) which simplifies to \(2 - x = 6 - \frac{1}{2}x\).

Step2: Add \(x\) to both sides

To get rid of the \(-x\) on the left, add \(x\) to both sides: \(2 - x + x = 6 - \frac{1}{2}x + x\), simplifying to \(2 = 6 + \frac{1}{2}x\).

Step3: Subtract 6 from both sides

Subtract 6 from both sides to isolate the term with \(x\): \(2 - 6 = 6 + \frac{1}{2}x - 6\), which gives \(-4 = \frac{1}{2}x\).

Step4: Multiply both sides by 2

To solve for \(x\), multiply both sides by 2: \(-4\times2 = \frac{1}{2}x\times2\), so \(x = -8\).

Answer:

\(-8\)