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Linear inequalities
Isolate the variable and account for the direction of the comparison sign.
Inequality Solver
Purpose-built solver page
Inequality Solver
Use this inequality solver for step-by-step reasoning about linear, compound, polynomial, rational, and absolute-value inequalities. Get the solution set explained in words or interval notation.
Type or upload a problemWorked explanationsNo sign-up required
Solve a problem nowinequality solver
x < 3
Linear inequalities
Compound inequalities
Polynomial and rational inequalities
inequality solver
Solve your inequality problem
Enter your inequality problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.
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inequality solver
What this Inequality 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.
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Compound inequalities
Handle AND/OR conditions and combine their solution sets correctly.
03
Polynomial and rational inequalities
Use critical points and sign analysis rather than treating them like ordinary equations.
04
Absolute-value inequalities
Translate distance statements into compound inequalities and test boundary cases.
Step
How to use the Inequality solver
A complete prompt usually produces a more useful explanation than an isolated expression.
−3x ≥ 6x ≤ −2- 1
Enter the complete inequality
−3x + 7 ≥ 19Use <, >, <=, or >= and include every part of a compound statement.
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Find boundary values
−3x + 7 = 19Solve the associated equality to identify where the sign can change.
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Track sign reversals
x ≤ −4Reverse the inequality when multiplying or dividing by a negative quantity.
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Express and test the set
(−∞, −4] · x = −5 ✓Write the result in inequality or interval notation and test a value from each interval.
Tip: ask for a named method, a domain, or a verification step when your course requires one.
inequality solver
Compound inequalities
Handle AND/OR conditions and combine their solution sets correctly.
Linear inequalities
x ≥ 2Isolate the variable and account for the direction of the comparison sign.
Compound inequalities
2 ≤ x < 7Handle AND/OR conditions and combine their solution sets correctly.
Polynomial and rational inequalities
(−∞, −5) ∪ (2, ∞)Use critical points and sign analysis rather than treating them like ordinary equations.
Absolute-value inequalities
|x| ≤ 4 ↔ −4 ≤ x ≤ 4Translate distance statements into compound inequalities and test boundary cases.
Example
Inequality problems to try
These examples reflect common search intent and can be inserted into the solver as a starting point.
Example 1
Solve -3x + 7 >= 19A linear inequality where division by a negative reverses the sign.
Example 2
Solve -2 < 3x + 1 <= 10A compound inequality requiring the same operation across all three parts.
Example 3
Solve (x - 2)(x + 5) > 0A polynomial inequality solved by critical points and sign intervals.
Formula guides
Understand the formulas used here
Review the related formulas, when to use them, and how they connect in a worked example.
Slope Formulas and Forms of a Line
Compare the slope formula, point-slope form, slope-intercept form, standard form, and special horizontal and vertical lines.
Open formula guideExponent Rules
Learn the product, quotient, power, zero, negative, and fractional exponent rules with examples and one complete simplification.
Open formula guideCommon mistakes to watch for
A worked answer is most useful when you know which details are easy to lose along the way.
Forgetting to flip the sign
Multiplying or dividing both sides by a negative reverses <, >, ≤, or ≥.
Keeping only boundary points
An inequality usually describes intervals, not just the values where equality holds.
Mixing AND with OR
Intersection and union produce different solution sets in compound inequalities.
Inequality solver FAQ
