Example 1
Solve |2x - 3| = 9A positive-distance equation with two linear cases.
Absolute Value Solver
Purpose-built solver page
Absolute Value Solver
Use this absolute value solver to work through absolute-value expressions, equations, and inequalities. The page emphasizes distance, case splitting, boundary conditions, and checking candidate solutions.
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|x - a|
Evaluate expressions
Absolute-value equations
Absolute-value inequalities
absolute value solver
Solve your absolute value problem
Enter your absolute value problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
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absolute value solver
What this Absolute Value solver is designed for
The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.
Evaluate expressions
|a| ≥ 0Simplify the quantity inside the bars before applying nonnegative distance.
Absolute-value equations
|A| = k → A = k ∨ A = -kSplit a positive-distance equation into its positive and negative cases.
Absolute-value inequalities
|A| < k → -k < A < kTranslate less-than cases to intersections and greater-than cases to unions.
Distance interpretation
|x-a| = rConnect |x-a| to distance from a point and interpret the result in context.
Step
How to use the Absolute Value solver
A complete prompt usually produces a more useful explanation than an isolated expression.
- 1
Isolate the absolute value
|A| ⋚ kMove other terms first so the absolute-value expression is by itself.
- 2
Inspect the comparison value
k < 0, k = 0, k > 0A negative right side can make an equation impossible or make an inequality always/never true.
- 3
Split into cases
A = ±k · -k < A < k · A < -k ∨ A > kWrite the correct two equations or compound inequalities.
- 4
Check each result
x ∈ ℝTest candidate solutions and confirm open or closed endpoints.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
Example
Absolute Value problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 2
Solve |x + 4| < 7A less-than inequality expressed as one compound interval.
Example 3
Solve |3x - 1| >= 5A greater-than inequality producing two outer intervals.
Formula guides
Understand the formulas used here
Review the related formulas, when to use them, and how they connect in a worked example.
Common mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Dropping the negative case
A positive absolute-value equation generally creates two cases, not one.
Using the wrong connector
Less-than distance uses AND; greater-than distance uses OR.
Ignoring an impossible value
An absolute value cannot equal a negative real number.
Absolute Value solver FAQ
