Question 11

-3x + 1 cannot equal 5 when |x|

Since |x| is constrained to values between -1 and 1, we can evaluate the expression -3x + 1. When x = 1, -3(1) + 1 equals -2, and when x = -1, -3(-1) + 1 equals 4. Therefore, the maximum output of -3x + 1 is 4, making it impossible for the expression to equal 5.

A) 5

This option cannot be the value of -3x + 1 because, as established, the maximum value of the expression, given the constraint |x|

B) 3

This option can be a value of -3x + 1. If we set -3x + 1 equal to 3, we find that -3x = 2, which implies x = -2/3. Since -2/3 falls within the range of |x|

C) 2

This option is also a possible value for -3x + 1. Setting -3x + 1 equal to 2 results in -3x = 1, leading to x = -1/3. This value satisfies the condition |x|

E) -1

This option can be a value of -3x + 1 as well. If we set -3x + 1 equal to -1, we find -3x = -2, which gives x = 2/3. This value meets the constraint of |x|

Conclusion

In conclusion, the value 5 is unattainable for the expression -3x + 1 under the condition |x|