x−6<x/4

To solve the inequality x - 6 < x/4, we can start by subtracting x from both sides of the inequality:

x - x - 6 < x/4 - x

Simplifying this, we have:

-6 < -3x/4

Next, we can multiply both sides of the inequality by -4/3 to maintain the inequality direction:

(-4/3)(-6) > (-4/3)(-3x/4)

Simplifying further, we get:

8 > x

Therefore, the solution to the inequality x - 6 < x/4 is x > 8.

To solve the inequality x - 6 < x/4, follow these steps:

Step 1: Eliminate the fractions by multiplying both sides of the inequality by 4:
4(x - 6) < x

Step 2: Distribute the 4 on the left side of the inequality:
4x - 24 < x

Step 3: Move all the terms containing x to one side of the inequality by subtracting x from both sides:
4x - x - 24 < 0
3x - 24 < 0

Step 4: Simplify the inequality:
3x < 24

Step 5: Divide both sides of the inequality by 3:
x < 24/3

Step 6: Simplify the expression:
x < 8

So, the solution to the inequality x - 6 < x/4 is x < 8.