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 77 ≤ 5 + 8n?

Back

To solve 77 ≤ 5 + 8n, first subtract 5 from both sides to get 72 ≤ 8n, then divide both sides by 8 to find n ≥ 9.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line, using open or closed circles to indicate whether endpoints are included.

Front

When graphing b < 6, what type of circle is used?

Back

An open circle is used when graphing b < 6, indicating that 6 is not included in the solution.

Front

What is the solution to the inequality -7x + 1 ≤ 22?

Back

The solution is x ≥ -3, found by isolating x through subtraction and division.

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be flipped.

Front

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

Back

To solve 2 - 3x ≤ 20, subtract 2 from both sides to get -3x ≤ 18, then divide by -3 (flipping the sign) to find x ≥ -6.

Front

What is the significance of an open circle on a number line?

Back

An open circle indicates that the number at that point is not included in the solution set of the inequality.

Front

What is the solution to the inequality 3x ≥ 12?

Back

The solution is x ≥ 4, found by dividing both sides by 3.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign means changing it from < to > or from ≤ to ≥, typically done when multiplying or dividing by a negative number.