counterexample if x less than or equal 6, then 2x-3 less than 9

There is only one:

x=6
2x-3=9 which is NOT less than 9.

To find a counterexample for the given statement "if x is less than or equal to 6, then 2x - 3 is less than 9," we need to find a value of x that satisfies the condition but does not satisfy the conclusion.

Let's start by assuming x is less than or equal to 6 and evaluate the expression 2x - 3 to see if it is less than 9.

For x = 6:
2(6) - 3 = 12 - 3 = 9

Since 9 is not less than 9, this does not serve as a counterexample.

For x = 5:
2(5) - 3 = 10 - 3 = 7

Again, 7 is not less than 9, so this is not the counterexample we're looking for.

For x = 4:
2(4) - 3 = 8 - 3 = 5

As 5 is less than 9, this also does not serve as a counterexample.

For x = 3:
2(3) - 3 = 6 - 3 = 3

Since 3 is less than 9, this does not provide the required counterexample.

For x = 2:
2(2) - 3 = 4 - 3 = 1

Finally, we have found a counterexample. When x = 2, the expression 2x - 3 is equal to 1, which is indeed less than 9. Therefore, x = 2 is the counterexample that disproves the statement.