find a counterexample to prove the following is false: x is less than or equal to 2x
To find a counterexample, we need to find a value of x for which the statement "x is less than or equal to 2x" is false. In other words, we need to find a value of x that violates this inequality.
Let's analyze the statement: "x is less than or equal to 2x." This inequality can be represented as x ≤ 2x. To find a counterexample, we need to find a value of x for which this inequality is not true.
Let's consider an example where x is negative. If we take x = -1 as an example, we have -1 ≤ 2(-1). Simplifying, -1 ≤ -2. However, this statement is false because -1 is not less than or equal to -2. Therefore, x = -1 serves as a counterexample to prove that the statement "x is less than or equal to 2x" is false.
In summary, the counterexample is x = -1.