Solve each equation and express the solutions in decimal...

Key Concepts

Decimal Arithmetic

Decimal arithmetic involves performing basic arithmetic operations—addition, subtraction, multiplication, and division—with numbers expressed in decimal form. Proficiency in decimal arithmetic is crucial for accurately solving equations and expressing the solutions in the correct format.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Solving linear equations involves isolating the variable on one side of the equation through a series of algebraic manipulations, ensuring that the equation remains balanced throughout the process.

Distributive Property

The distributive property is a mathematical rule used to multiply a single term by each term within a parenthesis. It allows the equation to be expanded so that operations can be performed on each term separately, making it easier to combine like terms and simplify the equation.

Combining Like Terms

Combining like terms is the process of simplifying equations by adding or subtracting terms that contain the same variable or are constants. By consolidating these terms, the equation becomes simpler, which is essential in isolating the variable and solving the equation.

Solution Verification

Solution verification is the process of substituting the obtained solution back into the original equation to ensure that it satisfies the equation. This step is important to confirm that no mistakes were made during the manipulations and that the answer is correct.

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