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 < 7, you would first subtract 3 and then divide by 2.

Front

How do you solve the inequality 77 ≤ 5 + 8n?

Back

First, subtract 5 from both sides: 77 - 5 ≤ 8n, which simplifies to 72 ≤ 8n. Then, divide both sides by 8: 9 ≤ n or n ≥ 9.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be either greater than or exactly equal to the number.

Front

When graphing the inequality a ≥ 11, what type of dot is used?

Back

A closed dot is used when graphing a ≥ 11 because the value 11 is included in the solution.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value is strictly less than the number.

Front

When graphing the inequality b < 6, would you use an open or closed circle?

Back

An open circle is used when graphing b < 6 because the value 6 is not included in the solution.

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 of an inequality by a negative number.

Front

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

Back

To solve 3x ≥ 12, divide both sides by 3: x ≥ 4.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value can be either less than or exactly equal to the number.

Front

How do you graph the inequality a < 11?

Back

To graph a < 11, draw a number line, place an open circle at 11, and shade to the left to indicate all values less than 11.