Solving & Graphing Multi-Step Inequalities

Front

What does the inequality x < -4 represent on a number line?

Back

The solution set includes all numbers less than -4, represented by an open circle at -4 and shading to the left.

Front

When solving the inequality -3x ≥ 12, what should you do with the inequality sign?

Back

You need to flip the inequality sign when dividing or multiplying by a negative number.

Front

How do you solve the inequality -3x + 2 ≤ 20?

Back

Subtract 2 from both sides to get -3x ≤ 18, then divide by -3 and flip the sign to get x ≥ -6.

Front

What is the first step to graph the solution set of the inequality -4n + 1 > -23?

Back

First, isolate n by subtracting 1 from both sides to get -4n > -24, then divide by -4 and flip the sign to get n < 6.

Front

When solving the inequality 3x ≥ -12, do you need to flip the inequality sign?

Back

No, you do not need to flip the inequality sign because you are dividing by a positive number.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary point, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary point.

Front

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

Back

Use an open circle for strict inequalities and a closed circle for non-strict inequalities, then shade the appropriate direction.

Front

What does it mean to 'flip' the inequality sign?

Back

Flipping the inequality sign means changing < to > or ≤ to ≥ (and vice versa) when multiplying or dividing both sides of the inequality by a negative number.

Front

What is the solution to the inequality 2x - 5 < 3?

Back

Add 5 to both sides to get 2x < 8, then divide by 2 to find x < 4.