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. For example, in the inequality 2x + 3 < 11, you would first subtract 3 and then divide by 2.

Front

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

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What symbol indicates an open dot when graphing an inequality?

Back

The symbols < and > indicate an open dot.

Front

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

Back

An open circle is used when graphing b < 6.

Front

How do you solve the inequality -3w - 2 < -17?

Back

Add 2 to both sides: -3w < -15. Then divide by -3 (remember to flip the inequality sign): w > 5.

Front

Do you need to flip the inequality sign when dividing by a negative number?

Back

Yes, you must flip the inequality sign when dividing or multiplying both sides by a negative number.

Front

What does it mean to graph an inequality?

Back

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

Front

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

Back

Divide both sides by 3: x ≥ 4.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included in the solution (e.g., < or >), while a closed circle indicates that the number is included (e.g., ≤ or ≥).

Front

How do you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it makes the inequality true.