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If you add or subtract the same number to both sides of an inequality, the inequality does not change direction.

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An inequality describes a region on the coordinate plane — not just a line.

To solve an inequality the first step is Graph the boundary line (use slope and intercept).

The second is Decide: solid or dashed line.

And the third one is Pick a test point → shade the side that satisfies the inequality.

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Common types of inequalities

-Linear: with unknowns of first degree.

-Quadratic: with squared unknowns.

-Rational: with algebraic fractions.

-Systems of inequations: two or more inequations that must be satisfied at the same time.

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To solve an inequality is like solving an equation:

You isolate the variable on one side.

Use addition, subtraction, multiplication, and division.

⚠️ Important Rule:
When you multiply or divide both sides by a negative number, you must reverse the inequality sign!

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An inequality (or inequation) is a mathematical statement that shows the relationship of order between two values or expressions.

It tells us which quantity is greater or smaller — unlike equations that show equality (=).

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Representación gráfica

Las soluciones se pueden representar en una recta numérica, usando puntos abiertos o cerrados, según el tipo de desigualdad.

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Key rules for solving inequalities

1-You can add or subtract the same values on both sides without changing the inequality.

2-Multiplying or dividing by a positive number does not change the direction of the inequality.

3-Multiplying or dividing by a negative number reverses the sign of the inequality.

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Solución de una inecuación

Resolver una inecuación significa encontrar todos los valores de la incógnita que hacen verdadera la desigualdad

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Diferencia con una ecuación

Una ecuación tiene una solución exacta, mientras que una inecuación puede tener infinitas soluciones que cumplen con la condición de desigualdad

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Inequality symbols

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An inequality is a mathematical expression that compares two quantities using inequality symbols instead of the equal sign.