Absolute value is a mathematical operation which results in the positive version of whatever number was placed inside its vertical brackets, like so: |-7| = 7. To write absolute value problems for yourself or your students, you have to work backwards. These problems ask the solver to find two values for x which satisfy an absolute value equation, such as 2*|x - 2| + 3 = 7. Once you have picked any two numbers for your solutions, you can create such an equation yourself.
Take the difference of the two solutions, subtracting the second from the first. Divide the result by 2. The result is the right-hand side of your equation.
Example: Use 1 and -3 as solutions. 1-(-3) = 4 4/2 = 2 2 is the right-hand side of the equation.
Set up and solve an algebraic equation with the first solution plus an unknown equal to the right-hand side of the equation. Use a different variable name than the one you plan to use in the final problem.
Example: 1 + y = 2 y = 1
Write a new equation combining the right-hand side and the y-value with an x in an absolute value expression.
Example: |x + 1| = 2
Solve the problem to double-check that your solutions work.
Example: |x + 1| = 2 x + 1 = 2 x = 1 -(x + 1) = 2 -x - 1 = 2 -x = 3 x = -3
If you wish, make the problem more complicated by performing operations to both sides of the equation.
Example: Multiply both sides by 2, then add 3 to both sides. 2_|x + 1| = 4 2_|x + 1| + 3 = 7
You can also create an absolute value inequality simply by changing the equals sign to an inequality sign.