Questions: Solve the inequality. x/4 > x + 6

Solution Steps

To solve the inequality \(\frac{x}{4} > x + 6\), we need to isolate \(x\) on one side. Start by eliminating the fraction by multiplying every term by 4. Then, move all terms involving \(x\) to one side of the inequality and constant terms to the other side. Finally, solve for \(x\).

Starting with the inequality

\[ \frac{x}{4} > x + 6, \]

we multiply every term by 4 to eliminate the fraction:

\[ x > 4(x + 6). \]

Distributing on the right side gives:

\[ x > 4x + 24. \]

Next, we rearrange the inequality by moving all terms involving \(x\) to one side:

\[ x - 4x > 24, \]

which simplifies to:

\[ -3x > 24. \]

Dividing both sides by -3 (and remembering to reverse the inequality sign) results in:

\[ x < -8. \]

Final Answer