FA 8-2: Two-Step Inequalities Word Problems

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 3x + 5 < 20, you would first subtract 5 from both sides and then divide by 3.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

When do you use a closed dot on a number line?

Back

You use a closed dot on a number line when graphing inequalities with '≤' or '≥', indicating that the endpoint is included in the solution.

Front

When do you use an open dot on a number line?

Back

You use an open dot on a number line when graphing inequalities with '<' or '>', indicating that the endpoint is not included in the solution.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Front

How can you represent a real-world situation with an inequality?

Back

You can represent a real-world situation with an inequality by identifying the maximum or minimum limits and expressing them mathematically. For example, if a person can spend no more than $100, you can write the inequality as x ≤ 100.

Front

What is the first step to solve the inequality 77 ≤ 5 + 8n?

Back

The first step is to subtract 5 from both sides of the inequality to isolate the term with the variable.

Front

How do you graph the solution of the inequality 3x + 20 ≤ 120?

Back

First, solve for x: 3x ≤ 100, then x ≤ 33.33. On a number line, place a closed dot at 33.33 and shade to the left.

Front

What is the inequality that represents the situation: 'A jacket costs $20 more than 3 times the price of a skirt, and the total must be no more than $120'?

Back

The inequality is 3x + 20 ≤ 120, where x is the price of the skirt.