Solving Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

An inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you represent the solution of an inequality on a number line?

Back

By using an open circle for < or > and a closed circle for ≤ or ≥, along with shading in the direction of the solution.

Front

What does the inequality k < 3 mean?

Back

It means that k can take any value less than 3.

Front

How do you solve the inequality -3 − 6(4x + 6) > -111?

Back

First, distribute -6, combine like terms, and isolate x to find x < 3.

Front

What does the inequality -2 ≥ n represent?

Back

It means that n can take any value that is less than or equal to -2.

Front

How do you solve the inequality 4(2a + 3) < 3(a - 1)?

Back

Distribute, combine like terms, and isolate a to find a < -3.

Front

What is the solution to the inequality 3(x - 2) < 2(x + 9)?

Back

The solution is x < 24.

Front

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

Back

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

Front

What does it mean to isolate the variable in an inequality?

Back

To manipulate the inequality so that the variable is on one side and all other terms are on the other side.

Front

What is the first step in solving a multi-step inequality?

Back

Identify and simplify any expressions on both sides of the inequality.