Solving Equations and Inequalities

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.

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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

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What does it mean to isolate a variable?

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Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side.

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What is the solution set of an equation?

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The solution set of an equation is the set of all values that satisfy the equation.

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What is the difference between a solution to an equation and a solution to an inequality?

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A solution to an equation is a specific value that makes the equation true, while a solution to an inequality is a range of values that satisfy the inequality.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

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What is the zero product property?

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The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

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How do you check if a solution is correct?

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To check if a solution is correct, substitute the solution back into the original equation or inequality and verify if it holds true.

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What is a common mistake when solving equations?

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A common mistake is to incorrectly apply operations, such as forgetting to distribute or incorrectly combining like terms.