The meaning of the Absolute Value Equation result
An absolute value equals c when its inside expression equals either c or −c. A positive c usually creates two linear branches.
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Absolute Value Equation Solver
Solve equations of the form |ax + b| = c and report both, one, or no real solutions. A checkable formula accompanies equation solutions instead of leaving an unexplained number.
Absolute Value Equation Solver inputs
Known quantities
Hand-checking the Absolute Value Equation result
A negative c has no solution because absolute value is nonnegative. If a=0, the equation is either always true or never true. If the Absolute Value Equation Solver assumptions do not fit, consider absolute-value inequality.
One complete Absolute Value Equation calculation
For |2x−3|=7, the branches 2x−3=7 and 2x−3=−7 give x=5 and x=−2.
Set ax+b=c and ax+b=−c, solve both linear equations, and remove any duplicate when c=0. A hand-worked extension of Absolute Value Equation Solver is solve each branch.
Questions Absolute Value Equation can resolve
These equations model fixed distance from a target, symmetric tolerances, and paired positions on a number line.
Boundary cases in Absolute Value Equation
A one-input Absolute Value Equation trial checks the expected behavior of absolute value equation solver.
Boundary checks for Absolute Value Equation
Substitute the Absolute Value Equation solution into Coefficient a. This Absolute Value Equation check rejects false Absolute Value Equation branches and forbidden denominators.
Choose an easy Coefficient a value before running Absolute Value Equation. Predict Constant b, then compare it with the Absolute Value Equation output.
Rework Absolute Value Equation without copying Equation solutions. Begin with Coefficient a and preserve Constant b. Predict the scale of the Absolute Value Equation answer, then compare it with Equation solutions. Store a changed Nonnegative right side c as another Absolute Value Equation case.
Cross-checking Absolute Value Equation
A boundary case can expose a Absolute Value Equation setup error. Choose a simple Coefficient a, preserve Constant b, and predict Equation solutions. If the new Equation solutions conflicts with that prediction, inspect the Absolute Value Equation entries before relying on the less convenient case.
Validating Absolute Value Equation
Challenge Equation solutions with a nearby value of Coefficient a. Leave Constant b fixed during the Absolute Value Equation trial. The direction of the new Equation solutions should agree with the underlying Absolute Value Equation relationship.
Questions about Absolute Value Equation
Why are there often two answers?
Two signed values have the same positive magnitude.
What if c=0?
There is one solution when a is nonzero.
Can c be negative?
Then there is no solution.
What if a=0?
The statement is either true for every x or for none.