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 the constraint |x| <= 1, the possible range for x is between -1 and 1. Substituting these limits into the expression -3x + 1 reveals that the maximum possible value it can achieve is 4, which makes 5 an unattainable result.

A (5) CORRECT

The expression -3x + 1 reaches a maximum of 4 when x = -1, as -3(-1) + 1 equals 4. Since 5 exceeds this maximum value, it cannot be produced by the given expression under the specified condition of |x| <= 1.

B (3) YOUR ANSWER

Substituting x = -1 gives -3(-1) + 1 = 4, and substituting x = 1 gives -3(1) + 1 = -2. The expression can take on the value of 3 when x = -2/3, since -3(-2/3) + 1 equals 3. Therefore, 3 is a possible outcome.

C (2) YOUR ANSWER

The expression can equal 2 when x = -1/3, as -3(-1/3) + 1 results in 2. Given the range of x, this value is achievable, thus making 2 a valid result.

D (0) YOUR ANSWER

When x = 1/3, -3(1/3) + 1 results in 0. This calculation shows that the expression can indeed yield 0, confirming its feasibility within the constraints.

E (-1) YOUR ANSWER

Substituting x = 2/3 results in -3(2/3) + 1 = -1. Hence, -1 is also a possible value for the expression within the given range of x.

Conclusion

In the scenario where |x| <= 1, the expression -3x + 1 can yield values ranging from -2 to 4. Among the provided options, only 5 exceeds this range, making it the only value that cannot be achieved under the given constraints. Thus, understanding the bounds of x is crucial for determining the possible outputs of the expression.

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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