Solving 2-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 2k - 9 ≤ -19?

Back

Add 9 to both sides to get 2k ≤ -10, then divide by 2 to find k ≤ -5.

Front

What is the solution to the inequality 16 - 4a > 8?

Back

Subtract 16 from both sides to get -4a > -8, then divide by -4 (remember to flip the inequality) to find a < 2.

Front

How do you solve the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides to get 7k ≥ -7, then divide by 7 to find k ≥ -1.

Front

What is the solution to the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Front

What does it mean to flip the inequality sign when dividing by a negative number?

Back

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

Front

What is the general form of a two-step inequality?

Back

The general form is ax + b < c, ax + b ≤ c, ax + b > c, or ax + b ≥ c, where a, b, and c are constants.

Front

How can you check your solution to an inequality?

Back

You can check your solution by substituting the solution back into the original inequality to see if it holds true.

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 the boundary point.

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.