absolute value inequality

Question

The inequality | x - 46.8 | < 2.7 describes the percentage of students who took the SATs during their junior year at Whitemore High School during the last five years. Find this range.

 

___% (<,>,≤,≥) x (<,>,≤,≥) ____%

Answer 1

| x - 46.8 | < 2.7

 

-2.7 < x - 46.8 < 2.7

 

Add 46.8 to all areas

 

44.1 < x < 49.5

 

 

Answer 2

If

 

x > 46.8,

 

then

 

x - 46.8 < 2.7

x < 49.5

 

If x < 46.8,

 

then

 

46.8 - x < 2.7

x > 44.1

 

Combine the 2 inequalities for x.

 

x < 49.5

x > 44.1 

 

The range for x is

 

44.1 < x < 49.5