Graphing Inequalities

Front

What is an inequality?

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 '≤' mean?

Back

'≤' 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

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph the inequality y > 2?

Back

To graph y > 2, draw a dashed horizontal line at y = 2 (indicating that 2 is not included) and shade the area above the line.

Front

How do you graph the inequality y ≤ -x + 3?

Back

To graph y ≤ -x + 3, first graph the line y = -x + 3 with a solid line (indicating that points on the line are included) and shade below 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 that points on the line are not included (> or <).

Front

What does the inequality x < -3 represent on a number line?

Back

The inequality x < -3 represents all numbers to the left of -3 on the number line, not including -3 itself.

Front

How do you solve the inequality 2x + 3 < 7?

Back

To solve 2x + 3 < 7, subtract 3 from both sides to get 2x < 4, then divide by 2 to find x < 2.

Front

What is the solution set for the inequality y ≥ 4?

Back

The solution set for y ≥ 4 includes all values of y that are 4 or greater, represented by a solid line at y = 4 and shading above.

Front

How do you interpret the graph of y < -2x + 1?

Back

The graph of y < -2x + 1 shows all points below the line y = -2x + 1, with a dashed line indicating that points on the line are not included.