∣x−10015∣∣≤23 where x is a person’s IQ. Solve the inequality to find the IQ scores for the middle 50% of the population.

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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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