**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.

After having gone through the stuff given above, we hope that the students would have understood "Two step equations with negative numbers".

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