Writing Inequalities & Equations 8.8A

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

How do you represent a cost comparison problem with an equation?

Back

You can represent a cost comparison problem by setting the total costs of two different options equal to each other, often involving variables to represent quantities.

Front

What does the variable 'x' typically represent in cost equations?

Back

In cost equations, 'x' usually represents the number of items or hours being purchased or rented.

Front

How do you solve for 'x' in the equation 0.79x + 24 = 1.19x?

Back

To solve for 'x', first isolate 'x' on one side of the equation by moving all terms involving 'x' to one side and constant terms to the other side.

Front

What is the first step in solving the equation 4x + 20 = 14x?

Back

The first step is to move all terms involving 'x' to one side of the equation, which can be done by subtracting 4x from both sides.

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What does it mean for two costs to be equal in a real-world scenario?

Back

It means that the total amount spent on both options is the same, allowing for a direct comparison of the two choices.

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What is the significance of the initial fee in a cost equation?

Back

The initial fee represents a fixed cost that must be paid regardless of the number of items or hours used, affecting the total cost calculation.

Front

How can you determine which option is cheaper based on an equation?

Back

By solving the equation for 'x', you can find the point at which the costs are equal, and then evaluate the costs for values of 'x' below and above that point.

Front

What is the purpose of writing equations in application-based problems?

Back

Writing equations helps to model real-world situations mathematically, allowing for analysis and solution of problems involving relationships between quantities.