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

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Key Concepts

Isolation of Variables

Isolation of variables refers to the process of rearranging the equation so that the variable appears on one side and the constants on the other. This is accomplished via inverse operations and is essential for finding the solution to the equation.

Combining Like Terms

Combining like terms involves adding or subtracting coefficients of the same variable to simplify an expression. This step streamlines the equation, making it easier to isolate the variable.

Working with Fractions

Working with fractions in equations requires careful manipulation including multiplying, dividing, and finding common denominators to combine terms. It ensures the equation is managed without losing precision during the solving process.

Linear Equations

Linear equations are algebraic equations in which each term is either a constant or the product of a constant and a single variable. They typically only involve operations of addition, subtraction, multiplication, and division, making it possible to solve for the variable using inverse operations.

Distributive Property

The distributive property allows one to multiply a term across a sum or difference inside parentheses, turning expressions such as a(b + c) into ab + ac. This is crucial for eliminating parentheses and simplifying the equation.

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