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. It typically involves addition or subtraction followed by multiplication or division.

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

How do you solve the inequality: -3x ≥ 12?

Back

Divide both sides by -3 and flip the sign: x ≤ -4.

Front

What does an open circle represent on a number line?

Back

An open circle indicates that the number is not included in the solution set (e.g., for b < 6).

Front

What does a closed circle represent on a number line?

Back

A closed circle indicates that the number is included in the solution set (e.g., for b ≤ 6).

Front

How do you graph the inequality 7n - 1 > 76?

Back

First, solve for n: 7n > 77, then n > 11. Graph with an open circle at 11 and shade to the right.

Front

What is the solution to the inequality -9a - 1 < 26?

Back

Add 1 to both sides: -9a < 27, then divide by -9 and flip the sign: a > -3.

Front

How do you isolate the variable in the equation 16 = k/11?

Back

Multiply both sides by 11 to isolate k: k = 176.

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 first step in solving a two-step inequality?

Back

The first step is usually to eliminate any constant term by adding or subtracting it from both sides.