Rewriting an equation is a fundamental skill in algebra and mathematics in general. It involves manipulating the equation to achieve a different but equivalent form. This can be useful for solving the equation, simplifying it, or making it easier to understand.
Basic Steps to Rewrite an Equation
- Identify the Goal
Before you start rewriting an equation, you need to know what you are trying to achieve. Are you solving for a specific variable? Are you trying to simplify the equation? Knowing your goal will guide your steps.
- Use Inverse Operations
To isolate a variable, use inverse operations. For example, if a variable is being added to a number, subtract that number from both sides of the equation. If it’s being multiplied, divide both sides by that number.
Example
Consider the equation:
$2x + 5 = 15$
To solve for $x$, follow these steps:
- Subtract 5 from both sides:
$2x + 5 – 5 = 15 – 5$
$2x = 10$ - Divide both sides by 2:
$frac{2x}{2} = frac{10}{2}$
$x = 5$
- Simplify the Equation
Combine like terms and simplify the equation as much as possible. This makes it easier to work with and understand.
Example
Consider the equation:
$3x + 4x – 2 = 12$
Combine like terms:
$7x – 2 = 12$
Add 2 to both sides:
$7x – 2 + 2 = 12 + 2$
$7x = 14$
Divide by 7:
$frac{7x}{7} = frac{14}{7}$
$x = 2$
- Check Your Work
After rewriting or solving the equation, always check your work. Substitute the solution back into the original equation to ensure it satisfies the equation.
Example
For the equation $2x + 5 = 15$ and solution $x = 5$:
Substitute $x = 5$ back into the original equation:
$2(5) + 5 = 15$
$10 + 5 = 15$
$15 = 15$
The solution is correct.
Conclusion
Rewriting an equation is a crucial skill in algebra, helping you solve, simplify, and understand mathematical problems. By following these steps and practicing regularly, you can become proficient in manipulating equations to achieve your desired form.