Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is not equal to the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the rule for flipping the inequality sign?

Back

The inequality sign flips when you multiply or divide both sides of the inequality by a negative number.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

Front

How do you represent a range of values in an inequality?

Back

A range of values can be represented using '≤' and '≥' symbols, such as 2 ≤ x ≤ 8.

Front

What does the inequality x < 5 mean?

Back

It means that x can be any number less than 5.

Front

How do you solve the inequality 3x + 2 < 11?

Back

Subtract 2 from both sides to get 3x < 9, then divide by 3 to find x < 3.

Front

What is the solution to the inequality -2x ≥ 6?

Back

Divide both sides by -2 (flipping the sign) to get x ≤ -3.

Front

What does the inequality x ≥ 4 represent?

Back

It represents all values of x that are greater than or equal to 4.

Front

How do you graph the inequality x < 3 on a number line?

Back

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