Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

To solve, subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does an open circle represent on a number line?

Back

An open circle indicates that the number is not included in the solution set (e.g., x < 3).

Front

What does a closed circle represent on a number line?

Back

A closed circle indicates that the number is included in the solution set (e.g., x ≤ 3).

Front

How do you graph the inequality x < 3?

Back

Graph an open circle at 3 and shade to the left to indicate all numbers less than 3.

Front

What inequality does the number line graph with a closed circle at -4 and shading to the left represent?

Back

The graph represents the inequality x ≤ -4.

Front

How do you solve the inequality 1 + 3r > 10?

Back

Subtract 1 from both sides: 3r > 9. Then divide by 3: r > 3.

Front

What does the inequality b ≤ -2 mean?

Back

It means that b can be -2 or any number less than -2.

Front

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

Back

Use open or closed circles to indicate whether endpoints are included, and shade the appropriate direction.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ means 'less than or equal to' (includes the endpoint), while < means 'less than' (does not include the endpoint).