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EXAMPLES & SOLUTIONS
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It is good to know the true value of a number when solving real-world problems.

Absolute value word problems are first created as an expression.
They are converted into equations to solve a problem.
ABSOLUTE WORD PROBLEM
Examples and explanations of how to solve absolute word problems

Word Problem

Water levels were measured by the sea. The first measurement was at 15 feet, the second measurement was at -10 feet, and the third water level measured -25 feet. Which water level is farthest from sea level (0 feet)? 

Measure 1                      15

Measure 2                   -10

Measure 3                  -25

Which measurement is furthest from sea level?
Measurement  3

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

Why is Measurement 3  the farthest from
sea level, eventhough 15 is the greatest
number and -25 is the least number?

Because it is the furtherest number from zero (sea level).
ABSOLUTE VALUE:
| -25 | = 25
| -25 | is further then 15

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

Word Problem

The Ireland meteorologist suggests that the temperature could be 5 (+5) degrees warmer or 5 (-5) degrees colder. If the temperature in Ireland is 30 degrees, what is the minimum and maximum temperature?

What is needed to discover the maximum and minimum temperatures?

Gathering Information

The variable is the unknown minimum and maximum values of the temperature in Ireland (n).
The constant is the initial degrees (30), and the degrees above and below (5).
The operator is the "-" sign.  It means "less than". It is the difference between the intial temp. and max/min temperatures.
The first term is the known number the degrees (5 above), the unknown temperature (n) and the total initial degrees (30). 
The second term is the known number the degrees (5 below), the unknown temperature (n) and the total initial degrees (30).

Components

Variables: n
Constant: 30, 5

Operator: '-'
Terms: 30, +5, n
Coefficient: 1

Expression:
30 - n |

Write the Equation

Maximum Temperature: n
"Less" means: '-'
Current Temperature: 30
Above zero: +5

| 30 - n | = +5

SOLVE THE EQUATION

      | 30 - n | = +5
      | 30 - n | = 30 - n
          30 - n = +5
30 - 30 - n = 5  - 30
      
  
         -n = -25

                   n = 25

-1        -1

Components

Variables: n
Constant: 30, 5

Operator: '-'
Terms: 30, -5, n
Coefficient: 1

Expression:
| 30 - n |

Write the Equation

Minimum Temperature: n
"Less" means: '-'
Current Temperature: 30
Below zero: -5

| 30 - n | = -5

SOLVE THE EQUATION

      | 30 - n | = -5
      | 30 - n | = 30 + n
          30 - n = -5
30 - 30 - n =  -5  - 30
      
  
         -n = -35

                   n = 35

-1        -1

CHECK YOUR ANSWER:

   | n - 30 | = +5
 | 35 - 30 | = +5
              | 5 | = 5
                  5 = 5


      35 --Solution

   | n - 30 | = -5
| 25 - 30 | = +5
           | -5 | = 5
                  5 = 5


25 --Solution

The difference in the temperature is always 5 degrees, no matter the direction. 
Hence, the absolute distance from 30 is 5 degrees.

The meteorologist suggest that the temperatures will be either 25 or 35 degrees

ABSOLUTE VALUE:
| -5 | = 5

-5

+5

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

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