If |x| < 1, which of the following CANNOT be the value of -3x + 1?

Rationale

5 cannot be the value of -3x + 1 when |x| < 1.

Given that |x| < 1, the possible range for x is -1 < x < 1. Therefore, substituting the extreme values into the expression -3x + 1 shows that the maximum value of -3x + 1 cannot reach 5, as it would require x to be less than -1.

A (5) CORRECT

To find the maximum of -3x + 1, we evaluate it at the limits of x. If x approaches 1, -3(1) + 1 = -2, and if x approaches -1, -3(-1) + 1 = 4. Since the maximum value we can achieve is 4, 5 is unattainable and thus cannot be a valid output.

B (3) YOUR ANSWER

When x is at its maximum of 1 (not inclusive), -3(1) + 1 equals -2, and at its minimum of -1 (not inclusive), -3(-1) + 1 equals 4. The value 3 lies within this range since it can be produced by an appropriate value of x, such as x = -1\3, resulting in -3(-1\3) + 1 = 3.

C (2) YOUR ANSWER

Similar to the previous choices, using x = -1\3 gives -3(-1\3) + 1 = 3, while using x = -1\2 yields -3(-1\2) + 1 = 2. Therefore, 2 is indeed a possible value of -3x + 1.

D (0) YOUR ANSWER

For x = 1\3, we find -3(1\3) + 1 = 0. This confirms that 0 can be achieved within the constraints of |x| < 1.

E (-1) YOUR ANSWER

By substituting x = 2\3, we get -3(2\3) + 1 = -1. Thus, -1 is achievable under the given condition.

Conclusion

In the expression -3x + 1, the constraints of |x| < 1 restrict the possible output values. While values such as 3, 2, 0, and -1 can be generated within that range, 5 exceeds the maximum limit of 4 established by the conditions. Therefore, the only value that cannot be reached is 5.

If |x| < 1, which of the following CANNOT be the value of -3x + 1?

5 cannot be the value of -3x + 1 when |x| < 1.

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