Solving Equations and Inequalities

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What does the inequality n > 6 represent in terms of solution sets?

Back

The solution set includes all real numbers greater than 6.

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What is the Distributive Property in mathematics?

Back

The Distributive Property states that a(b + c) = ab + ac, allowing you to distribute a multiplier across terms in parentheses.

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How do you solve the equation 3x + 15 = 3(x + 5)?

Back

By simplifying both sides, you find that the equation is true for all values of x, resulting in infinitely many solutions.

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What does the equation 45w + 123.95 = 753.95 represent in a real-world context?

Back

It represents the total cost Erica paid for dance classes, where 45 is the weekly fee and 123.95 is the registration fee.

Front

How can you graph the inequality n > 6?

Back

You would draw a number line, shading to the right of 6, indicating that all numbers greater than 6 are included.

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What is an equation?

Back

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

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

What is the difference between a solution set and a graph of an inequality?

Back

A solution set is the collection of all possible solutions to an equation or inequality, while a graph visually represents those solutions on a number line or coordinate plane.

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What does it mean for an equation to have infinitely many solutions?

Back

It means that there are countless values for the variable that satisfy the equation, often occurring when both sides of the equation are equivalent.

Front

What is the first step in solving a linear equation?

Back

The first step is often to isolate the variable by performing inverse operations on both sides of the equation.