Chapter 8.7, Problem 63HP

To determine

Use a counter example for all values of x; two times x is greater than x is true or false?

Answer to Problem 63HP

When x is positive, the statement is a true statement but when x is negative the statement is a false statement.

Explanation of Solution

Given:

Use a counter example for all values of x; two times x is greater than x is true or false?

Concept Used:

When $x=2,\text{ then }2·2=4\Rightarrow 4> 2$

If x is positive then two times x is greater than x is a true statement.

When $x=–2,\text{ then }2·(-2)=–4\Rightarrow –2> –4$

If x is negative, and then two times x is greater than x is a false statement.

Thus, when x is positive, the statement is a true statement but when x is negative the statement is a false statement.