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 represent a situation where a total amount is limited by an inequality?

Back

You can represent it by forming an inequality that includes the total amount spent or received and the maximum limit.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating 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', indicating that the value on the left can be greater than or equal to the value on the right.

Front

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

Back

An open circle is used when graphing b < 6 to indicate that 6 is not included in the solution set.

Front

How do you solve a two-step inequality?

Back

To solve a two-step inequality, first isolate the variable by performing the inverse operations in the reverse order of operations, and then simplify the inequality.

Front

What is the first step in solving the inequality 0.20x + 5 ≤ 12?

Back

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

Front

What does it mean for a variable to be 'greater than' in an inequality?

Back

It means that the value of the variable must exceed a certain number, not including that number itself.

Front

How can you express a situation where a person has a certain amount of money and receives more in terms of an inequality?

Back

You can express it by adding the amount received to the initial amount and setting it greater than a target amount.

Front

What is the significance of the inequality 106 - 4x ≤ 70 in a real-world context?

Back

This inequality represents a situation where a dog needs to lose weight over a number of weeks to reach a target weight.