If x > 3 and x < 7, which of the following is true?

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Question: If x > 3 and x < 7, which of the following is true?

Options:

Correct Answer: x - 1 < 5

Solution:

Since x is between 3 and 7, x - 1 will be between 2 and 6, thus x - 1 < 5 is true.

If x > 3 and x < 7, which of the following is true?

If x > 3 and x < 7, which of the following is true?

Step 1: Understand the given information. We know that x is greater than 3 and less than 7. This can be written as 3 < x < 7.
Step 2: Determine the range of x. Since x is between 3 and 7, we can find the minimum and maximum values for x.
Step 3: Calculate x - 1. If we subtract 1 from x, we need to find the new range. If x is 3, then x - 1 is 2. If x is 7, then x - 1 is 6.
Step 4: Establish the new range. Therefore, x - 1 is between 2 and 6, which can be written as 2 < x - 1 < 6.
Step 5: Check the statement x - 1 < 5. Since x - 1 can be as high as 6, we need to see if it can be less than 5.
Step 6: Since the maximum value of x - 1 is 6, it can also be less than 5 when x is between 3 and 5. Therefore, x - 1 < 5 is true for some values of x.

Inequalities – Understanding and manipulating inequalities to determine the range of possible values for a variable.
Algebraic Manipulation – Applying basic algebraic operations to derive new inequalities from existing ones.