Solving Inequalities

Front

What is an inequality?

Back

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

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 solution set of an inequality?

Back

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

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

Solve: 3(x - 2) < 2(x + 9)

Back

x < 24

Front

Solve: 5z - 2 - 2z < 13

Back

z < 5

Front

Solve: 10 ≥ x - 3

Back

x ≤ 13

Front

If 15 > x - 1, what are possible values for x?

Back

Possible values for x are 1, 7, 15.

Front

What does it mean to 'flip the sign' in an inequality?

Back

Flipping the sign means changing the direction of the inequality symbol when multiplying or dividing by a negative number.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is strictly larger, while 'greater than or equal to' (≥) includes the value itself.