Final answer:
Option C, 3(x - 5), is the correct answer because when x=5, it results in 0, which is less than the value of the given expression evaluated at 49 when completed as 2x² - 1.
Step-by-step explanation:
The student asked which expression has a value less than the given expression when x = 5. To find out, we need to evaluate each option at x = 5 and compare them.
- A) 4x + 54: Substituting x with 5, we get 4(5) + 54 = 20 + 54 = 74.
- B) x + 5: Substituting x with 5, we get 5 + 5 = 10.
- C) 3(x - 5): Substituting x with 5, we get 3(5 - 5) = 3(0) = 0.
- D) 2x² + 5: Substituting x with 5, we get 2(5)² + 5 = 2(25) + 5 = 50 + 5 = 55.
To find out which expression is less than the value of the given expression, first, we need to evaluate the given expression itself. As per the information provided, we have:
If we complete the square in x², this condition simplifies to 2 (x² − ¹)² ≤ which we can solve to obtain 4’
We have a bit of a typo or missing information here, so let's assuming the intended expression is 2x² - 1. When x = 5, the expression evaluates to 2(5²) - 1 = 50 - 1 = 49.
Comparing all the calculated values, option C) 3(x - 5) is the only one that results in a value less than 49 when x = 5, which makes it the correct answer.