Free Online Calculator

Inequality Solver

Name: Inequality Solver
Author: AskMathAI

Solve inequalities effortlessly with our step-by-step calculator. Get instant solutions and detailed explanations for inequalities like $2x + 3 > 7$ , $x² - 4 \leq 0$ .

Inequality Calculator

Enter your inequality and get step-by-step solutions

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Master Inequalities with Our Advanced Solver

Our inequality solver is designed to help students, teachers, and professionals solve mathematical inequalities efficiently. Whether you're working on algebra homework, preparing forSAT exams, or tackling university mathematics courses, this tool provides comprehensive step-by-step solutions that enhance your understanding of inequality solving techniques.

The algebra solver online handles various types of inequalities including linear inequalities like $ax + b > c$ , quadratic inequalities like $x² - 4 \leq 0$ , and compound inequalities. This inequality calculator can process different formats including fractions, decimals, and complex expressions. Our math solver is particularly useful for SAT preparation, where understanding inequality solutions is crucial for success.

Perfect for high school algebra students learning the fundamentals, college studentsin calculus prerequisites, and professionals who need quick mathematical solutions. Theinequality solver provides not just answers, but detailed explanations that help you understand the underlying concepts and improve your problem-solving skills.

Types of Inequalities

Type of Inequality	Example	Solution	Difficulty Level
Linear Inequality	$2x + 3 > 7$	$x > 2$	Beginner
Quadratic Inequality	$x² - 4 \leq 0$	$-2 \leq x \leq 2$	Intermediate
Compound Inequality	$1 < x < 5$	$x \in (1, 5)$	Intermediate
Fractional Inequality	$\frac{1}{x} > 2$	$0 < x < \frac{1}{2}$	Advanced
Absolute Value	$\|x - 3\| < 2$	$1 < x < 5$	Intermediate

Common Mistakes to Avoid

Forgetting to Reverse Inequality

When multiplying or dividing both sides by a negative number, remember to reverse the inequality sign. For example, $-2x > 6$ becomes $x < -3$ .

Ignoring Domain Restrictions

For fractional inequalities like $\frac{1}{x} > 2$ , always check that the denominator is not zero and consider the domain restrictions.

Not Testing Solution

Always test your solution by substituting values from your answer back into the original inequality to verify it's correct.

How to Solve Inequalities

An inequality is a mathematical statement that compares two expressions using inequality symbols. The general form for a linear inequality is:

$ax + b > c$

where $a$ , $b$ , and $c$ are constants, and $x$ is the variable we need to solve for. The inequality symbol can be $>$ , $<$ , $\geq$ , or $\leq$ .

Step-by-Step Method

Isolate variable

Move all terms containing the variable to one side

Combine like terms

Simplify the expression by combining similar terms

Solve for variable

Divide both sides by the coefficient of the variable

Check direction

Remember to reverse inequality when dividing by negative

Key Rule

$\text{When multiplying/dividing by negative: } > \leftrightarrow <, \geq \leftrightarrow \leq$

Examples

Linear Inequality

$2x + 3 > 7$

Solution:

Subtract 3 from both sides: $2x > 4$
Divide both sides by 2: $x > 2$

$x > 2$

Negative Coefficient

$-3x + 6 ≤ 12$

Solution:

Subtract 6 from both sides: $-3x \leq 6$
Divide by -3 (reverse inequality): $x \geq -2$

$x ≥ -2$

Compound Inequality

$1 < 2x - 3 < 7$

Solution:

Add 3 to all parts: $4 < 2x < 10$
Divide all parts by 2: $2 < x < 5$

$2 < x < 5$

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Frequently Asked Questions

What is an inequality?

An inequality is a mathematical statement that compares two expressions using symbols like >, <, ≥, or ≤. Unlike equations, inequalities have solution sets rather than single values.

How do I solve inequalities with negative coefficients?

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign. For example, -2x > 6 becomes x < -3.

What's the difference between < and ≤?

< means "less than" (not including the boundary), while ≤ means "less than or equal to" (including the boundary). The same applies to > and ≥.

Can inequalities have multiple solutions?

Yes, inequalities typically have solution sets rather than single values. For example, x > 2 means all real numbers greater than 2.

Is this calculator free to use?

Yes, our inequality solver is completely free to use with no limitations. You can solve as many inequalities as you need.

How accurate are the solutions?

Our calculator provides highly accurate solutions with step-by-step explanations. It handles both exact fractions and decimal approximations.

Inequality Solver

Inequality Calculator

Master Inequalities with Our Advanced Solver

Types of Inequalities

Common Mistakes to Avoid

Forgetting to Reverse Inequality

Ignoring Domain Restrictions

Not Testing Solution

How to Solve Inequalities

Step-by-Step Method

Isolate variable

Combine like terms

Solve for variable

Check direction

Key Rule

Examples

Linear Inequality

Solution:

Negative Coefficient

Solution:

Compound Inequality

Solution:

Try Our AI Math Solver

Frequently Asked Questions

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