Unit 2 - Solving Multistep 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

How do you graph an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

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

Back

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

Front

How do you isolate a variable in an inequality?

Back

Use inverse operations to move terms away from the variable, similar to solving an equation.

Front

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

Back

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

Front

Solve the inequality: -3 - 6(4x + 6) > -111

Back

x < 3

Front

Write an inequality for spending at most $1200 on a laptop after a $400 down payment.

Back

12x + 400 < 1200

Front

Solve the inequality: 4(2a + 3) < 3(a - 1)

Back

a < -3