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 in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, y ≥ 2 means y is greater than or equal to 2.

Front

How do you graph the inequality y > 2x - 5?

Back

To graph y > 2x - 5, first graph the line y = 2x - 5 as a dashed line, then shade the area above the line.

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 they are not included (> or <).

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 point's coordinates into the inequality. If the inequality holds true, the point is a solution.

Front

What does the inequality y ≤ -x + 1 represent graphically?

Back

The inequality y ≤ -x + 1 represents the area below and including the line y = -x + 1.

Front

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

Back

The solution set of x > -5 includes all real numbers greater than -5.

Front

How do you graph the inequality y < 1/2x + 2?

Back

To graph y < 1/2x + 2, graph the line y = 1/2x + 2 as a dashed line and shade the area below the line.

Front

What does the inequality y ≥ -3x + 4 indicate about the line?

Back

The inequality y ≥ -3x + 4 indicates that the area above and including the line y = -3x + 4 is part of the solution.