Question

Let F(x) be the statement "x + 1 > 2x." Is the following statement true or false if the domain consists of all integers?

true or false

Answer 1

The statement 'x + 1 > 2x' is true if the domain consists of all integers.

Step-by-step explanation:

The statement is true if the domain consists of all integers. To determine if the statement is true, we can test it for a few values of x. Let's start by substituting x = 0 into the inequality: 0 + 1 > 2(0). Simplifying, we get 1 > 0, which is true. We can also test x = 1 and x = -1, and we will find that the statement holds true for all integers.

Therefore, the statement 'x + 1 > 2x' is true if the domain consists of all integers.