Formulate and Solve Absolute Value

The average temperature in January in a northern Canadian city is 1 degree Farenheit. The actual January temperature for that city may be about 5 degrees warmer or colder. Write an equation to find the minimum and maximum temperature.

y= | x - ​ (a)   | = ​ (b)  

• 1
• 5
• 6
• -5
• -1
• -6

• 690
• 6
• 696
• -6
• 5
• 4
• 3
• 2
• 1
• 689

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Which of the following inequalities can be used to assess which if his salary is tolerable? (m is the measure of the salary)

• |m - 500| ≤ 3000
• |m - 500| ≥ 3000
• |m - 3000| ≥ 500
• |m - 3000| ≤ 500

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x-50|=15
• |x+15|=50
• |50+x|=15
• No Solution

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03
• |v-20|=0.03
• |v|-0.03=20
• |v-0.03|=20

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12