Solve for x: 4(2-x)>8x+20

divide each side by 4

2-x>2x+5

add x to each side
2>3x+5
subtract five from each side
-3>3x
divide by 3
-1>x

or x<-1 x is less than -1

To solve for x in the inequality 4(2 - x) > 8x + 20, we can follow these steps:

Step 1: Distribute the 4 on the left side of the inequality:
8 - 4x > 8x + 20

Step 2: Group the x terms on one side and the constant terms on the other side.
-4x - 8x > 20 - 8

Step 3: Combine like terms:
-12x > 12

Step 4: Divide both sides of the inequality by -12 (remember that when dividing or multiplying by a negative number, the inequality sign flips):
x < 12/(-12)

Simplifying further:
x < -1

Therefore, the solution to the inequality 4(2 - x) > 8x + 20 is x < -1.