1. Equations are mathematical statements that assert two expressions are equal

2. A linear equation in one variable has the form $ax + b = 0$, where $x$ is the variable, and a and b are real coefficients, with a≠0.

3. Clear Fractions Using LCM:

• If the equation contains fractions, clear them by finding the Least Common Multiple (LCM) of the denominators. Multiply every term of the equation by this LCM to eliminate fractions.

4. Simplify Both Sides:

• Combine like terms on each side of the equation to simplify it. This involves adding or subtracting terms that have the same variable or constants.

5. Isolate the Variable:

• Move the variable term to one side of the equation and the constant terms to the other side. Use inverse operations (addition/subtraction, multiplication/division) to accomplish this:
  • Addition/Subtraction: To move constants, use the inverse operation (e.g., add or subtract).
  • Multiplication/Division: To move coefficients of the variable, divide or multiply as necessary.

6. Solve for the Variable:

• Perform the necessary operations to isolate the variable and solve for its value. This usually involves simplifying both sides of the equation until the variable is alone on one side.

7. Verify the Solution:

• Substitute the solution back into the original equation to ensure both sides are equal. This confirms the correctness of the solution.

like:

1. Solve for ( x ): $2x + 5 = 11$

• Subtract 5 from both sides: ( 2x = 6 )
• Divide by 2: ( x = 3 )

Conclusion: By following these steps clearing fractions, simplifying, isolating the variable, solving, and verifying you can effectively solve linear equations in one variable.