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, or not equal to the other.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

What is a solution set?

Back

A solution set is the set of all values that satisfy a given equation or inequality.

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What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions if any value of the variable makes the equation true, often seen in identities.

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How do you check if a solution is correct?

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To check a solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one and graphs as a straight line.

Front

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

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A strict inequality (e.g., <, >) does not include the boundary value, while a non-strict inequality (e.g., ≤, ≥) does include it.