When faced with a mathematical equation, the goal is to find the value of the unknown variable that makes the equation true. In this article, we will explore how to solve an equation step by step, ensuring we understand how to select the correct answer.
Understanding the Equation
An equation is a mathematical statement that asserts the equality of two expressions. For example:
[ 2x + 3 = 11 ]
In this equation, (x) is the unknown variable we want to solve for.
Steps to Solve the Equation
Step 1: Isolate the Variable
The first step in solving an equation is to isolate the variable on one side. In our example, we need to move the constant (3) to the other side:
- Subtract 3 from both sides:
[ 2x + 3 - 3 = 11 - 3 ]
This simplifies to:
[ 2x = 8 ]
Step 2: Solve for the Variable
Now that we have isolated (2x), we need to solve for (x) by dividing both sides by 2:
[ \frac{2x}{2} = \frac{8}{2} ]
This simplifies to:
[ x = 4 ]
Step 3: Verify the Solution
It’s crucial to check our solution by substituting (x) back into the original equation:
[ 2(4) + 3 = 11 ]
Calculating gives:
[ 8 + 3 = 11 ]
Since both sides equal 11, our solution (x = 4) is indeed correct.
Selecting the Correct Answer
When presented with multiple-choice answers, follow these guidelines:
- Understand the question: Read carefully what is being asked.
- Perform calculations: Use the above steps to solve for the variable.
- Check all answers: If multiple options seem plausible, substitute each option back into the original equation to see which one satisfies it.
- Eliminate wrong choices: If you find any options that do not satisfy the equation, eliminate them to narrow down your choices.
Conclusion
Solving equations involves isolating the variable and verifying the solution. By following the systematic steps outlined in this article, you can confidently select the correct answer when faced with an equation. Always remember to double-check your work to ensure accuracy. Happy solving!
