Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -9a - 1 < 26?

Back

To solve -9a - 1 < 26, first add 1 to both sides to get -9a < 27, then divide by -9 (remember to flip the inequality sign) to find a > -3.

Front

When do you flip the inequality sign?

Back

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

Front

What does an open circle represent on a number line?

Back

An open circle represents that the number is not included in the solution set, indicating a strict inequality (e.g., < or >).

Front

What does a closed circle represent on a number line?

Back

A closed circle represents that the number is included in the solution set, indicating a non-strict inequality (e.g., ≤ or ≥).

Front

How do you graph the inequality b < 6?

Back

To graph b < 6, place an open circle on 6 and shade to the left, indicating all values less than 6.

Front

What is the solution to the inequality 25 < X - 10?

Back

To solve 25 < X - 10, add 10 to both sides to get 35 < X, or X > 35.

Front

What is the solution to the inequality X ≥ 4?

Back

The solution to X ≥ 4 includes all values of X that are 4 or greater, represented by a closed circle at 4 and shading to the right.

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 the boundary value.

Front

How do you check the solution of an inequality?

Back

To check the solution of an inequality, substitute a value from the solution set back into the original inequality to see if it holds true.