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.
An absolute value equals c when its inside expression equals either c or −c. A positive c usually creates two linear branches.
This definition sets the boundary between absolute value equation solver and a neighboring calculation with similar inputs.
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.
For |2x−3|=7, the branches 2x−3=7 and 2x−3=−7 give x=5 and x=−2.
These equations model fixed distance from a target, symmetric tolerances, and paired positions on a number line.
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.
A one-input Absolute Value Equation trial checks the expected behavior of absolute value equation solver.
A field name is part of the formula. Match the problem's quantities to coefficient a, constant b and nonnegative right side c, then check that they share the scale assumed by the absolute value equation solver relationship.
Increasing c moves the two solution points farther apart around the center −b/a. This is a stronger check than judging the answer only by how many decimal places it shows.
Match the reported precision to coefficient a, constant b and nonnegative right side c, not to the number of digits the browser can display. Preserve an exact form when it communicates the absolute value equation solver structure more clearly than a decimal.
An absolute-value inequality describes an interval or exterior region rather than isolated solution points. The formula panel makes the chosen definition explicit.
The minimum audit trail is short: coefficient a, constant b and nonnegative right side c, their units, and the formula beside the answer. It is enough to distinguish this calculation from a similar-looking shortcut.
Two signed values have the same positive magnitude.
There is one solution when a is nonzero.
Then there is no solution.
The statement is either true for every x or for none.