Answer:
Starting with the given inequality:
-4(r - 2/3) + 4 < -8
First, simplify the expression inside the parentheses:
-4r + 8/3 + 4 < -8
Combine the constants:
-4r + 20/3 < -8
Subtract 20/3 from both sides:
-4r < -8 - 20/3
-4r < -24/3 - 20/3
-4r < -44/3
Finally, divide both sides by -4, remembering to reverse the direction of the inequality since we are dividing by a negative number:
r > -44/3 ÷ -4
r > 11/3
So the solution to the inequality is r > 11/3, which means that any value of r that is greater than 11/3 will make the inequality true.