Question

These expressions are equivalent ( the same value)

4 > x < 1
4>x and x>1
A. True
B. False

Answer 1

The expressions 4 > x < 14>x and x > 1 are not equivalent. The values of x that satisfy both conditions are between 1 and 4, excluding 1 and 4 themselves.

Step-by-step explanation:

The expressions 4 > x < 14>x and x > 1 are not equivalent.

Let's analyze the first expression: 4 > x < 14>x. This expression can be broken down into two separate inequalities: 4 > x and x < 14. This means that x must be less than 4 and at the same time, less than 14. Looking at the number line, we can see that the values of x that satisfy these conditions are between negative infinity and 4.

Now, let's analyze the second inequality: x > 1. This means that x must be greater than 1. Looking at the number line again, we can see that the values of x that satisfy this condition are between 1 and infinity.

The intersection of the solutions for the two inequalities is the values of x that satisfy both conditions. In this case, it is the values of x between 1 and 4, excluding 1 and 4 themselves. Therefore, the expressions are not equivalent and the answer is False.