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.