negative 4 is less than or equal to 4 times left parenthesis 6 y minus 12 right parenthesis minus 2 y
The given expression is:
-4 ≤ 4(6y - 12) - 2y
Let's simplify it step by step:
-4 ≤ 24y - 48 - 2y
Combine like terms:
-4 + 48 ≤ 24y - 2y
44 ≤ 22y
Divide both sides by 22 (since it is a positive value):
2 ≤ y
Therefore, the solution is y ≥ 2.
To determine if -4 is less than or equal to 4 times (6y - 12) - 2y, we can follow these steps:
Step 1: Distribute the 4 to the terms inside the parentheses:
4 * (6y - 12) = 24y - 48
Step 2: Simplify the equation by combining like terms:
24y - 48 - 2y = 22y - 48
Step 3: Now we have the equation -4 <= 22y - 48
Step 4: To solve for y, we isolate the variable:
-4 + 48 <= 22y
44 <= 22y
Step 5: Divide both sides of the equation by 22 to solve for y:
44/22 <= y
2 <= y
So, y is greater than or equal to 2.