Solve the inequality and graph the solution.

9(x+2)>9(x-3)

my work:
9x+18>9x-27
+27 +27
____________
9x+45>9x
-9x -9x
____________
45>0

I found it to come out to 45>0.. but that can't be right. What am I doing wrong?

But since 45 is always greater than 0, wouldn't all real numbers be solutions?

yes, any real number will work in your inequation.

To solve the inequality and graph the solution, let's first go through the steps:

Step 1: Distribute the 9 to both terms inside the parentheses on the left side of the inequality:
9(x + 2) > 9(x - 3)
9x + 18 > 9x - 27

Step 2: Simplify both sides of the inequality:
9x + 18 > 9x - 27

At this point, you correctly subtracted 9x from both sides to isolate the constant term on one side:

9x - 9x + 18 > 9x - 9x - 27
18 > -27

However, you made a mistake in your final conclusion:

You wrote "45 > 0," but the correct outcome is "18 > -27."

Now, let's interpret the result correctly:

Step 3: Simplify further:
18 > -27

So, the inequality states that 18 is greater than -27.

Since this inequality is true for all values of x, the solution interval is (-∞, +∞) or all real numbers.

Now, let's graph the solution on a number line:

To graph the solution interval (-∞, +∞), we represent this as a number line that extends infinitely in both the negative and positive directions.

Since there is no specific value or range of values for x, the graph represents all real numbers.

On the number line, we label the line with arrows on both ends, indicating the graph extends indefinitely in both directions.

---------------------------------------------------->
-∞ +∞

So, the graph of the solution is a number line with arrows at both ends, indicating that the solution to the given inequality includes all real numbers.

Some inequalites will have no answer. You just have to show your work and put "No answer"

:)