When solving linear equations, what is the first step you should take?

When solving linear equations, what is the first step you should take?

• A. Isolate the variable by applying inverse operations to both sides of the equation.
• B. Combine like terms.
• C. Multiply both sides by the coefficient.
• D. Check the solution.

Answer: (A)

Isolating the variable by applying inverse operations to both sides is the first step because it clears away constants and other attached terms, leaving the unknown alone so you can solve for it directly. For example, with 3x + 5 = 20, subtracting 5 from both sides gives 3x = 15, and then dividing by 3 gives x = 5. The rule is to undo whatever was done to the variable: add or subtract to move numbers to the other side, and multiply or divide to move the coefficient away. Once the variable is isolated, you can check your solution by substituting it back. Combining like terms can help with simplification, but it isn’t always possible or the first move. Multiplying both sides by the coefficient is just a specific instance of removing a multiplier and isn’t the universal starting step. Checking the solution is important, but it comes after you’ve found a value for the variable.

Isolating the variable by applying inverse operations to both sides is the first step because it clears away constants and other attached terms, leaving the unknown alone so you can solve for it directly. For example, with 3x + 5 = 20, subtracting 5 from both sides gives 3x = 15, and then dividing by 3 gives x = 5. The rule is to undo whatever was done to the variable: add or subtract to move numbers to the other side, and multiply or divide to move the coefficient away. Once the variable is isolated, you can check your solution by substituting it back.

Combining like terms can help with simplification, but it isn’t always possible or the first move. Multiplying both sides by the coefficient is just a specific instance of removing a multiplier and isn’t the universal starting step. Checking the solution is important, but it comes after you’ve found a value for the variable.