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 variables.

Front

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 does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find the range of values for the variable that makes the inequality true.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation and the constant on the other.

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What is a solution set?

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A solution set is the set of all values that satisfy a given equation or inequality.

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What does it mean if an equation has infinitely many solutions?

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An equation has infinitely many solutions if any value of the variable makes the equation true, often occurring when both sides of the equation are equivalent.

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What is a common mistake when solving equations?

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A common mistake is incorrectly applying operations, such as adding instead of subtracting or misapplying the distributive property.

Front

What is the first step in solving the equation 3x + 15 = 3(x + 5)?

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The first step is to apply the distributive property to simplify the right side: 3(x + 5) becomes 3x + 15.