Final answer:
The correct ways to transform an equation into an equivalent one include substitution, addition, division, multiplication, factoring, and combining like terms, each method maintaining the balance and integrity of the original equation.
Step-by-step explanation:
The correct answer is option A) Substitution, Addition, Division, Multiplication, Factoring, Combining Like Terms. These methods are fundamental in transforming an equation into an equivalent one. To start:
- Substitution allows us to replace a variable with its value or another expression.
- Addition or Subtraction involves adding or subtracting the same quantity on both sides of the equation to maintain balance.
- In Division or Multiplication, both sides of the equation are divided or multiplied by the same non-zero number, preserving the equation's equality.
- Factoring is rewriting an expression as the product of its factors, which can simplify the equation solving process.
- Combining Like Terms involves adding or subtracting terms with the same variable and exponent.
Each of these techniques is used to manipulate equations to make them easier to solve. It’s crucial to perform the same operation on both sides of the equation to keep them equivalent. Additionally, always check your answer to ensure its reasonableness - does it make sense within the context of the problem?