Inequalities Unit 8 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, greater than or equal to, or less than or equal to the other.

Front

How do you represent a situation where one quantity is greater than another using an inequality?

Back

You can represent it using the 'greater than' symbol (>), for example, if x is greater than y, it is written as x > y.

Front

What is the general form of a linear inequality in one variable?

Back

The general form is ax + b > c, ax + b < c, ax + b ≥ c, or ax + b ≤ c, where a, b, and c are constants.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation.

Front

What does it mean to graph a linear inequality on a number line?

Back

Graphing a linear inequality on a number line involves shading the region that represents all possible solutions, using an open circle for < or > and a closed circle for ≤ or ≥.

Front

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

Back

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

Front

How can you check if a solution to an inequality is correct?

Back

You can check by substituting the solution back into the original inequality to see if it holds true.

Front

What is a compound inequality?

Back

A compound inequality is formed when two inequalities are combined, typically using 'and' or 'or' to connect them.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, solve each inequality separately and then combine the solutions, ensuring to consider the type of conjunction (and/or) used.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable, affecting the direction of the inequality.