Graphing Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade in the direction indicated by the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How do you determine the solution set of a linear inequality?

Back

To determine the solution set of a linear inequality, graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality, similar to solving an equation, and remember to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What is a boundary line in the context of graphing inequalities?

Back

A boundary line is the line that represents the equation of the inequality, dividing the graph into two regions.

Front

What does it mean if a point is above the boundary line in a graph of an inequality?

Back

If a point is above the boundary line, it means that the point satisfies the inequality if the inequality is of the form y > mx + b or y ≥ mx + b.