Absolute Value Inequalities
Word Problems
Ex 1
Write an equation involving the absolute value for the graph
Find the point that is the same distance from –4 as the distance from 6.
The midpoint between –4 and 6 is 1.
The distance from 1 to –4 is 5 units.
The distance from 1 to 6 is 5 units.
So, an equation is
x -1 = 5
#2 Ex.
On your basketball team, the starting players’ scoring averages are
between 6 and 10 points per game. Write an absolute-value inequality
describing the scoring averages for the players.
Step 1: Write as a compound inequality
6  x  10
Step 2: Find the half way point and subtract from each part
Half way between 6 and 10 is 8
6  8  x  8  10  8
 2  x 8  2
Step 3: Re-write as an absolute value inequality
x 8  2
The average number of points scored by the starting basketball
players was 8 points per game and they varied by 2 points per
game.
#3 Ex.
Your car averages 32 miles per gallon in the city. The actual mileage
varies from the average by at most 5 miles per gallon.
A) Write an absolute-value inequality that shows the
range for the mileage your car gets.
B)
x  32  5
Between what two numbers does the gas mileage range.
 5  x  32  5
27  x  37
The car ranges between 27 and 37 miles per gallon.