-4(2n-6)<n+6
-4(2n-6)<n+6
-8n + 24 < n + 6
-9n < -18
n > 2
remember that when dividing by a negative, the inequality sign has to be reversed.
Next step is -8n +24 < n + 6
Then subtract 24 from both sides to get -8n < n - 18 Then subtract n from both sides to get -9n < -18 then divide by -9 and make sure you flip the sign since you're dividing by a negative to get n>2
To solve the inequality -4(2n-6)<n+6, we can use the rules of solving inequalities. Let's go through the steps:
Step 1: Distribute -4 to the terms inside the parentheses:
-8n + 24 < n + 6
Step 2: Simplify the equation by combining like terms:
-8n - n < 6 - 24
-9n < -18
Step 3: Divide both sides of the inequality by -9. Since we are dividing by a negative number, the direction of the inequality sign will be reversed:
n > -18 / -9
Step 4: Simplify the expression on the right side of the inequality:
n > 2
Therefore, the solution to the inequality -4(2n-6)< n+6 is n > 2.