Solving Inequalities with Multiplication and Division

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 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 reverse the inequality sign.

Front

Solve the inequality: -8x < -48

Back

x > 6

Front

Solve the inequality: -5m < 10

Back

m > -2

Front

Solve the inequality: -4m > -8

Back

m < 2

Front

Solve the inequality: x/4 > -3

Back

x > -12

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

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side of the number line.

Front

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

Back

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