Graphing Inequalities

Front

What is an inequality in mathematics?

Back

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

Front

What does the symbol '≥' represent?

Back

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

Front

What does the symbol '≤' represent?

Back

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

Front

How do you graph the inequality x > 3?

Back

To graph x > 3, draw a number line, place an open circle at 3 (indicating that 3 is not included), and shade the line to the right to indicate all numbers greater than 3.

Front

How do you graph the inequality y < -2?

Back

To graph y < -2, draw a number line, place an open circle at -2 (indicating that -2 is not included), and shade the line downwards to indicate all numbers less than -2.

Front

What is the difference between a solid circle and an open circle on a graph?

Back

A solid circle indicates that the number is included in the solution (≥ or ≤), while an open circle indicates that the number is not included (> or <).

Front

What does the inequality r ≥ -6 represent on a number line?

Back

The inequality r ≥ -6 represents all numbers greater than or equal to -6, including -6 itself, which is shown with a solid circle at -6 and shading to the right.

Front

How can you determine which graph corresponds to a given inequality?

Back

To determine which graph corresponds to a given inequality, identify the boundary point, check whether it is included (solid or open circle), and observe the direction of shading.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line represents the values that satisfy the equality part of the inequality. Depending on whether the inequality is strict or inclusive, the line may be solid or dashed.

Front

What does the inequality b ≥ -1.5 indicate about the value of b?

Back

The inequality b ≥ -1.5 indicates that b can be any value greater than or equal to -1.5.