Linear Inequalities Review

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 (such as <, >, ≤, or ≥).

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

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

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for < or > inequalities).

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (used for ≤ or ≥ inequalities).

Front

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

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between 'y < 2x + 3' and 'y ≤ 2x + 3'?

Back

'y < 2x + 3' means the line is dashed and does not include points on the line, while 'y ≤ 2x + 3' means the line is solid and includes points on the line.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that are considered together. The solution is the region where the shaded areas of all inequalities overlap.

Front

How do you find the intersection of two inequalities?

Back

To find the intersection of two inequalities, graph both inequalities and identify the region where their shaded areas overlap.