Concept (1)

Solving for a variable in absolute value equations follows different rules than when we solve multi-step equations. When solving absolute value equations, most of the time we get more than one possible solution. Using absolute value equations, we are able to solve more complex concepts such as absolute values with inequalities, and graphs of absolute value inequalities with two variables.

Sample Problems (9)

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Solve for x.

3|x − 4| = 12
Problem 1
How to solve equations with absolute values when there are two solutions.

Solve for x.

-2|x − 3| + 3= -5
Problem 2
How to solve equations with absolute values when dividing by a negative number.

Solve for x.

|2x + 3| − 4 = -4
Problem 3
How to solve equations with absolute values when the absolute value equals zero.

Solve for x.

|2x + 1| + 10 = 3
Problem 4
How to solve equations with absolute values when the absolute value equals a negative number.
Problem 5
Solving absolute value equations by replacing the absolute value sign with +, - parentheses.
Problem 6
Solving absolute value equations by making the constant positive and negative.
Problem 7
Determining the number of solutions to an absolute value equation.
Problem 8
Write the absolute value equation from given solutions.
Problem 9
Solving absolute value equations by replacing the absolute value signs with + - ( ) and solving two equations.