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, or not equal to the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you graph the inequality y < x/5 - 3/2?

Back

To graph y < x/5 - 3/2, first graph the line y = x/5 - 3/2 as a dashed line, then 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

How do you determine the solution set for the inequality x + 2y ≤ 6?

Back

To determine the solution set, graph the line x + 2y = 6 as a solid line and shade below the line.

Front

What does the inequality y < -2 represent graphically?

Back

The inequality y < -2 represents all points below the horizontal line y = -2.

Front

How do you solve the inequality y ≤ -2x?

Back

To solve y ≤ -2x, graph the line y = -2x as a solid line and shade below the line.

Front

What is the solution set for the inequality x ≥ -2?

Back

The solution set for x ≥ -2 includes all points to the right of the vertical line x = -2, including the line itself.

Front

What does the inequality y > -1/2x + 3 represent?

Back

The inequality y > -1/2x + 3 represents all points above the dashed line y = -1/2x + 3.