Answer:
Step-by-step explanation:
Given the expression
∣x−10015∣∣≤23, we are to find the range of values of x
since the function is in a modulus sign, it can be expressed as a negative and positive function.
If the function is positive;
x - 10015 ≤23
x ≤23 + 10015
x ≤ 10038
If the function is negative;
-(x-10015)≤23
-x+10015≤23
-x≤23-10015
-x≤-9992
multiply through by -1
x ≥ 9992 (note the inequality sign change)
9992≤x
Combine both inequalities
9992≤x and x ≤ 10038
On combining;
9992≤x 10038
Hence the inequality to find the IQ scores for the middle 50% of the population is expressed as 9992≤x 10038
We want to solve an inequality to find the range of IQ scores for half of the population.
We will find that the range is:
77.15 ≤ x ≤ 123.15
The inequality we need to solve is:
|x - 100.15| ≤ 23
To solve it, we write two inequalities.
x - 100.15 ≤ 23
x - 100.15 ≥ -23
Solving these two, we will get the maximum and minimum of the range.
The maximum is given by:
x - 100.15 ≤ 23
x ≤ 23 + 100.15 = 123.15
The minimum is given by:
x - 100.15 ≥ -23
x ≥ -23 + 100.15 = 77.15
Then the range is:
77.15 ≤ x ≤ 123.15
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