TWO STEP EQUATIONS WITH NEGATIVE NUMBERS

Many real-world quantities such as altitude or temperature involve negative numbers. We solve equations with negative numbers just as we do equations with positive numbers.

Example 1 : 

To convert a temperature from degrees Fahrenheit to degrees Celsius, first subtract 32. Then multiply the result by 5/9. An outdoor thermometer showed a temperature of -10 °C. What was the temperature in degrees Fahrenheit ?

Solution : 

Step 1 :

Let x represent the temperature in degrees Fahrenheit.

Write an equation.

-10  =  (5/9).(x - 32)

Step 2 : 

Solve the equation.

Multiply both sides by 9/5

(9/5).(-10)  =  (9/5).(5/9).(x - 32)

-18  =  x - 32

Add 32 to both sides.

-18 + 32  =  x - 32 + 32

14  =  x

Hence, the temperature was 14 degrees Fahrenheit.

Example 2 : 

What is the temperature in degrees Fahrenheit of a freezer kept at -20 °C?

Solution : 

Step 1 :

Let x represent the temperature in degrees  Fahrenheit. 

Write an equation.

-20  =  (5/9).(x - 32)

Step 2 : 

Solve the equation.

Multiply both sides by 9/5

(9/5).(-20)  =  (9/5).(5/9).(x - 32)

-36  =  x - 32

Add 32 to both sides.

-36 + 32  =  x - 32 + 32

-4  =  x

Hence, the temperature was -4 degrees Fahrenheit.

Example 3 : 

An airplane flies at an altitude of 38,000 feet. As it nears the airport, the plane begins to descend at a rate of 600 feet per minute. At this rate, how many minutes will the plane take to descend to 18,800 feet ?

Solution : 

Step 1 :

Let m represent the number of minutes. Write an  equation. 

38,000 - 600m  =  18,800

Step 2 : 

Subtract 38,000 from both sides.

(38,000 - 600m) - 38,000  =  18,800 - 38,000 

-600m  =  -19,200

Divide both sides by -600

(-600m)/(-600)  =  (-19,200)/(-600)

m  =  32

Hence, the plane will take 32 minutes to descend to 18,800 feet.

Example 4 : 

Jenny earned 92 of a possible 120 points on a test. She lost 4 points for each incorrect answer. How many incorrect answers did she have?

Solution : 

Step 1 :

Let m represent the number of incorrect answers. Write an  equation. 

120 - 4m  =  92

Step 2 : 

Subtract 120 from both sides.

(120 - 4m) - 120  =  92 - 120 

-4m  =  -28

Divide both sides by -4

(-4m)/(-4)  =  (-28)/(-4)

m  =  7

Hence, Jenny had 7 incorrect answers. 

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