Simplifying expressions with negative variables
When a variable has a negative value, the main goal is to substitute carefully and then simplify the signs in the correct order.
1) Replace the variable
- Put the given negative value in place of the variable.
- Use parentheses around the negative number, especially if it is next to a minus sign or inside a product.
2) Simplify the signs
- If you multiply two negative numbers, the result is positive.
- A minus in front of a negative quantity becomes a plus: for example, (-(-a) = a).
- Keep the order of operations: parentheses, then multiplication/division, then addition/subtraction.
3) Finish the arithmetic
- Combine like terms if there are any.
- Write the result in simplest form.
4) Check your work
- Re-read the original expression and confirm every negative value was enclosed correctly.
- If possible, evaluate the expression a second time using the sign rules to see whether the result matches.
A good habit is to write each step separately instead of trying to do everything in your head. That makes it much easier to avoid sign mistakes.