12/5 - Review - Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed (for < or >) or solid line (for ≤ or ≥). Then, shade the region that satisfies the inequality.

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

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

Back

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

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does the inequality symbol '>' mean?

Back

'>' means that the value on the left is greater than the value on the right, excluding the right value.

Front

What does the inequality symbol '<' mean?

Back

'<'' means that the value on the left is less than the value on the right, excluding the right value.

Front

What does the inequality symbol '≥' mean?

Back

'≥' means that the value on the left is greater than or equal to the value on the right, including the right value.

Front

What does the inequality symbol '≤' mean?

Back

'≤' means that the value on the left is less than or equal to the value on the right, including the right value.

Front

If the inequality is y < -2/5x - 4, where do you shade?

Back

You shade below the line because the inequality symbol is '<'.