How do I solve linear equations?
Understand the Problem
The question is asking for guidance on how to solve linear equations, which typically involves steps such as isolating the variable, combining like terms, and applying inverse operations.
Answer
$x = 4$
Answer for screen readers
The solution to the equation is $x = 4$.
Steps to Solve
- Isolate the variable Start by rewriting the equation to isolate the variable on one side. If your equation is something like $2x + 3 = 11$, you would first subtract 3 from both sides of the equation.
$$ 2x + 3 - 3 = 11 - 3 $$
This simplifies to:
$$ 2x = 8 $$
- Divide to solve for the variable Now, divide both sides by the coefficient of the variable, which in this case is 2.
$$ \frac{2x}{2} = \frac{8}{2} $$
This simplifies to:
$$ x = 4 $$
- Check your solution It's always a good idea to check your solution by substituting it back into the original equation to ensure it works. If you substitute $x = 4$ back into the original:
$$ 2(4) + 3 = 11 $$
which simplifies to:
$$ 8 + 3 = 11 $$
Since both sides are equal, your solution is verified.
The solution to the equation is $x = 4$.
More Information
In solving linear equations, we often isolate the variable to find its value, which helps in solving real-world problems like calculating distances, speeds, or amounts in various contexts.
Tips
- Forgetting to perform the same operation on both sides of the equation, which can lead to incorrect solutions. Always maintain balance in the equation.
- Not checking the solution can result in missing errors in calculations. Always substitute your answer back into the original equation to verify.
AI-generated content may contain errors. Please verify critical information
