Solving Equations and Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What symbols are used to represent inequalities?

Back

The symbols used to represent inequalities include: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Front

What does a closed dot on a number line indicate when graphing inequalities?

Back

A closed dot indicates that the number is included in the solution set, used for inequalities with ≤ or ≥.

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What does an open dot on a number line indicate when graphing inequalities?

Back

An open dot indicates that the number is not included in the solution set, used for inequalities with < or >.

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What is the Division Property of Equality?

Back

The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.

Front

How do you solve the equation 1 + a = 15?

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To solve for a, subtract 1 from both sides: a = 15 - 1, which simplifies to a = 14.

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How do you solve the equation 3 = c - 1?

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To solve for c, add 1 to both sides: c = 3 + 1, which simplifies to c = 4.

Front

What is the purpose of graphing inequalities?

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Graphing inequalities visually represents the solution set on a number line, helping to understand which values satisfy the inequality.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary points, while a non-strict inequality (≤ or ≥) includes the boundary points.