Mastering Compound and Multi-Step Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to a specified number.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than', indicating that the value must be strictly greater than a specified number.

Front

How do you graph the solution to an inequality?

Back

To graph the solution to an inequality, use a number line, placing a closed circle for '≤' or '≥' and an open circle for '<' or '>'. Shade the appropriate direction based on the inequality.

Front

What is the solution to the inequality -2x + 3 ≤ 7?

Back

The solution is x ≥ -2.

Front

How do you interpret the solution x > 7?

Back

The solution x > 7 means that any value greater than 7 satisfies the inequality.

Front

What is the first step in solving the inequality 4x - 5 > 3x + 2?

Back

The first step is to isolate the variable x by subtracting 3x from both sides.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if the two sides cannot be made equal or if the conditions contradict each other.