Solving Inequalities and Graphing Systems of Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

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Back

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

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What does it mean for a system of equations to have one solution?

Back

A system has one solution when the graphs of the equations intersect at exactly one point.

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What does it mean for a system of equations to have infinite solutions?

Back

A system has infinite solutions when the equations represent the same line, meaning they overlap completely.

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What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over the run between two points on the line.

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How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.