Inequalities Test Review

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. Examples include <, >, ≤, and ≥.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' 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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that satisfies the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How do you solve the inequality 5(v + 3) - 10v > -10?

Back

First, simplify: 5v + 15 - 10v > -10. Combine like terms: -5v + 15 > -10. Then, isolate v: -5v > -25, so v < 5.

Front

What does the inequality -3 ≤ 2x - 1 ≤ 5 represent?

Back

This compound inequality means that 2x - 1 is greater than or equal to -3 and less than or equal to 5. To solve, isolate x: -1 ≤ x ≤ 3.

Front

How do you model a real-world scenario with an inequality?

Back

Identify the relationship described, assign a variable to the unknown, and write an inequality that represents the situation. For example, 'Four times a number increased by 6 is greater than 22' can be modeled as 4x + 6 > 22.

Front

What is the difference between '>' and '≥'?

Back

The symbol '>' means 'greater than' and does not include the endpoint, while '≥' means 'greater than or equal to' and includes the endpoint.

Front

How do you solve the compound inequality 24 > -3r > -9?

Back

To solve, divide all parts by -3 (remember to flip the inequality signs): -8 < r < 3.

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.