Solving Absolute Value Equations
Solving Absolute Value Inequalities
Solving Absolute Value Inequalities w/ Trivial Solutions
Absolute Value Equations from Solution Set
Application Problems
100
lx+5l=10
What is {-15, 5}
100
l1+bl<4
What is {b<3 and b>-5}?
100
|x - 3| > -5
What is All Real Numbers?
100
{-4, 6}
What is |x - 1|=5?
100
A teacher has test scores for a class modeled by the equation below (where x is the score a student obtains):|x - 82| ≥ 9 What is the average test score?
What is 82%?
200
2|x + 7| - 5 = - 5
What is {-7}?
200
l10p - 4l<34
What is {p<19/5 and p>-3}?
200
|5 - x| < - 4
What is No Solutions?
200
{3, 7}
What is |x - 5| = 2?
200
A teacher has test scores for a class modeled by the equation below (where x is the score a student obtains):|x - 82| ≥ 9 What are the highest and lowest test scores?
What is 91 (high) and 73 (low)?
300
5 - |4 - x| = 13
What is No Solution?
300
2lx + 3l>8
What is {x<-7 or x>1}?
300
2 - |3 + x| > 5
What is No Solutions?
300
{-14, -8}
What is |x + 11|=3?
300
A caterpillar needs to maintain a core temperature between (can include) 54℉ and 68℉ in order to survive its metamorphosis in its cocoon. Write an absolute value inequality to model the temperature in x ℉ of a caterpillar which survives its metamorphosis.
What is |x - 61| <= 7?
400
6l1 - 5xl - 9=57
What is {-2, 12/5}?
400
2lx+2l-1<8
What is {x<1 and x>-5}?
400
3|x + 4| - 1 > 11
What is {x > 0 or x < - 8}?
400
{-10, 15}
What is |x - 2.5|=12.5?
400
Buffalo Wild Wings has discounted prices on boneless wings for children and senior citizens. A customer is considered a child if they are 14 years old or younger and a senior citizen if they are 56 or over. Write an absolute value inequality to model the age range of customers that are not eligible for the discounted prices.
What is |x - 35| < 21?
500
l3x+2l=4x+5
What is {-1}? x = -3 is extraneous
500
2lx + 9l+3>7
What is {x>-7 or x<-11}?
500
3 - 2|x - 11| < 4
What is All Real Numbers?
500
{68, 133}
What is |x - 100.5|=32.5?
500
A mechanical engineer designs an air-conditioning system which activates a boiler/AC unit only when the temperature of the building is either below 66° or above 78°. This saves energy costs, and is less stress on the system. Let x be the temperature (in degrees) of the building. Write an absolute value inequality to model when the system would be turned off given x.
What is |x - 72| <= 6?
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