Answer: the value of x is 34.
Step-by-step explanation: Let's start by finding the mode of the set of integers. The mode is the number that appears most frequently in the set.
From the given integers, we can see that x appears twice, and all other numbers appear only once. Therefore, the mode is x.
Now we are told that the mean of the set is 1.5 times the mode. We can set up an equation to represent this:
(mean) = 1.5 * (mode)
To find the mean, we can add up all the numbers in the set and divide by the total number of integers:
(mean) = (31 + 58 + 98 + x + x) / 5
Simplifying the expression on the right:
(mean) = (187 + 2x) / 5
Substituting this expression for the mean into our equation:
(187 + 2x) / 5 = 1.5x
Multiplying both sides by 5 to eliminate the fraction:
187 + 2x = 7.5x
Subtracting 2x from both sides:
187 = 5.5x
Dividing both sides by 5.5:
x = 34
Therefore, the value of x is 34.