Solve each equation. Leave your answer as a fraction if it...

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Key Concepts

Linear Equations

Linear equations involve expressions where the variable is raised only to the first power. Solving them requires understanding how to manipulate the equation with the goal of isolating the variable on one side, which ultimately leads to finding its value.

Inverse Operations

Inverse operations are techniques used to undo operations applied to a variable in an equation. For example, if a constant is added to the variable term, you subtract that constant from both sides of the equation; similarly, multiplication can be undone by division. This concept is essential for maintaining the equality while isolating the variable.

Working with Fractions

When variables in equations are multiplied by fractions, it is often necessary to manage these fractions carefully by either multiplying both sides of the equation by the reciprocal of the fraction or by finding a common denominator. This ensures that the equation is simplified properly, allowing for accurate isolation of the variable and yielding the correct solution.

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