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 '≤' represent in inequalities?

Back

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

Front

What does the symbol '≥' represent in inequalities?

Back

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

Front

How do you graph the inequality x < -4?

Back

To graph x < -4, draw a number line, place an open circle at -4, and shade to the left to indicate all values less than -4.

Front

What is the solution to the inequality 8 - 3k < 8(1 - 7k)?

Back

The solution is k < 0.

Front

How do you solve the inequality -4x + 12 ≤ 60?

Back

First, subtract 12 from both sides to get -4x ≤ 48. Then, divide by -4 (remember to flip the inequality sign) to get x ≥ -12.

Front

What does the graph of the inequality 2 > p look like?

Back

The graph of 2 > p shows an open circle at 2 with shading to the left, indicating all values less than 2.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.

Front

How do you represent the solution set of an inequality on a number line?

Back

The solution set is represented by shading the region of the number line that satisfies the inequality, using open or closed circles to indicate whether the endpoints are included.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.