Compound and Linear Inequalities

Front

What is a compound inequality?

Back

A compound inequality consists of two or more inequalities joined by the words 'and' or 'or'. For example, x < 3 and x > 1.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to another value.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

In 'and' inequalities, both conditions must be true simultaneously. In 'or' inequalities, at least one condition must be true.

Front

How do you graph the inequality y ≤ -¾x - 1?

Back

To graph y ≤ -¾x - 1, first graph the line y = -¾x - 1 as a dashed line, then shade below the line.

Front

What does a dashed line represent in graphing inequalities?

Back

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

Front

What does a solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (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, substitute the x and y values into the inequality. If the inequality holds true, the point is a solution.

Front

What is the solution set of the inequality x ≤ -2 OR x > 5?

Back

The solution set includes all values of x that are less than or equal to -2 and all values greater than 5.

Front

What does the inequality y ≥ -3 represent on a graph?

Back

The inequality y ≥ -3 represents all points on or above the horizontal line y = -3.

Front

How do you write an inequality for a given graph?

Back

To write an inequality for a graph, identify the boundary line and determine if it is solid or dashed, then express the region that is shaded.