Final answer:
The reason for each step in the solution of an equation includes the use of the distributive property, combining like terms, inverse operations, and factoring. These steps help simplify and isolate the variable to find the solution.
Step-by-step explanation:
The reason for each step in the solution of an equation is as follows:
- Distributive Property: This step allows us to distribute a number or variable to each term inside parentheses. For example, in the equation 2(3x + 5) = 14, we can distribute the 2 to both terms inside the parentheses: 6x + 10 = 14.
- Combining Like Terms: This step involves combining or simplifying terms that have the same variables and exponents. For example, in the equation 6x + 10 = 14, we can combine the 6x and 10 to get 6x + 10 - 10 = 14 - 10, which simplifies to 6x = 4.
- Inverse Operations: This step involves undoing the operations that were done to the variable to isolate and solve for it. For example, in the equation 6x = 4, we can divide both sides by 6 to isolate x: (6x)/6 = 4/6, which simplifies to x = 2/3.
- Factoring: Factoring is a technique used to break down a polynomial equation into its factors. It is useful when solving quadratic equations or simplifying expressions. For example, in the equation x^2 - 5x + 6 = 0, we can factor it as (x - 2)(x - 3) = 0.