Answer:
No solutions.
Explanation:
Pre-Solving
Given
We are given the inequality 6(x+3) < 3(2x+6), and we want to solve the inequality for x.
Solving
We can first do the distributive property on both sides, where we multiply each term on the left side by 6, and each term on the right by 3.
6(x+3) < 3(2x+6)
6x + 18 < 6x + 18
Solving inequalities is a lot like solving equations; we want to isolate the variable by itself on one side.
First, we can subtract 18 from both sides.
6x + 18 < 6x + 18
-18 -18
____________________
6x < 6x
Now, we can subtract 6x from both sides, to get 6x off the right side.
6x < 6x
-6x -6x
0 < 0
We now have the inequality 0 < 0. This is never true, as 0 is always equal to 0.
Therefore, there are no values of x that will make this true, because no matter what, we will end up with a false statement. The answer is no solutions.