Question

Write an inequality comparing it to 19 and choose the same as a possible solution. Write an inequality comparing it to 41 algebraically.

a) x<19, x>41
b) x≤19, x≥41
c) x>19, x<41
d) x≥19, x≤41

Answer 1

The correct inequalities that compare x to 19 and 41 algebraically are in options c) and d), either x>19, x<41 if x is strictly between 19 and 41, or x≥19, x≥41 if 19 and 41 are included as possible values for x.

Step-by-step explanation:

The student has asked to write an inequality comparing x to 19 and choose the same as a possible solution, as well as writing an inequality comparing x to 41 algebraically. To do this, we have to compare x with both 19 and 41 and provide the appropriate inequality symbols. Looking at the options:

• a) x is less than 19 and greater than 41, which is not possible.
• b) x is less than or equal to 19 and greater than or equal to 41, which is again not possible.
• c) x is greater than 19 and less than 41, which is a possible range of values for x.
• d) x is greater than or equal to 19 and less than or equal to 41, which is also a possible range of values for x.

Considering the logical possibilities, we can conclude that the correct answer is either option c) or d) as they both present a valid range where x could lie. If x must be strictly between 19 and 41, then c) is correct, but if 19 and 41 are included in the possible values of x, then d) would be the right choice.