Solution set
CONCEPTS
Method to Solve Absolute Values
1) Isolate the absolute value on 1 side of the equation.
2) If there is a variable inside the absolute value
• Create 2 algebraic equations by setting any expression that has a variable in the absolute value expression equal to + or – that expression.
• Use AND to show there are 2 sets of solutions.
Tips
• If there is an inequality and you divide by a negative, then change the inequality sign
(ex: -5x > 10 => x < 2)
PRACTICE PROBLEMS
Question 1 4x + 6 = |-4|. What is x?
-- Answer -- x = 1/2 or -1/2
4 = -4x - 6, x = 2 / 4 = 1/2 OR
4 = 4x + 6, x = -2 / 4 = -1/2
Question 2 What are the potential values of x for the expression |x - 1| < B
-- Answer -- x < B + 1 & x > -B + 1 OR -B + 1 < x < B + 1
(x - 1) < B -> x < B + 1
-(x - 1) < B -> (x - 1) > -B -> x > -B + 1
Question 3 Write an absolute value equation that has the solution which is the set of all real #'s that are 2 units from 2?
-- Answer -- x = 0, 4
x - 2 = 2, x = 4
-(x - 2) = 2, -x + 2 = 2, x = 0
ACT PRACTICE PROBLEMS
