x-6<x/4 solve for x inequality

Answer 1

To solve the inequality \( x - 6 < \frac{x}{4} \), follow these steps:

1. Eliminate the fraction by multiplying both sides of the inequality by 4 (the denominator):

   \[ 4(x - 6) < x \]

   This simplifies to:

   \[ 4x - 24 < x \]

2. Rearrange the inequality by subtracting \( x \) from both sides:

   \[ 4x - x - 24 < 0 \]

   Which simplifies to:

   \[ 3x - 24 < 0 \]

3. Add 24 to both sides of the inequality:

   \[ 3x < 24 \]

4. Divide both sides by 3:

   \[ x < 8 \]

Thus, the solution to the inequality \( x - 6 < \frac{x}{4} \) is:

\[ \boxed{x < 8} \]