Write the expression in simplest form. 8.95x+7.5-2.4x-6.3
The correct answer and explanation is:
To simplify the expression 8.95x + 7.5 – 2.4x – 6.3, follow these steps:
- Group like terms: Combine the terms that contain the variable x and the constant terms separately.
- The terms with x are 8.95x and -2.4x.
- The constant terms are 7.5 and -6.3.
- Combine the variable terms:
Add or subtract the coefficients of x: 8.95x−2.4x=(8.95−2.4)x=6.55×8.95x – 2.4x = (8.95 – 2.4)x = 6.55x - Combine the constant terms:
Add or subtract the constants: 7.5−6.3=1.27.5 – 6.3 = 1.2 - Write the simplified expression:
After combining like terms, the simplified expression is: 6.55x+1.26.55x + 1.2
This expression is in its simplest form because we have combined the terms in the most efficient way, leaving us with just one term for the variable x and one constant.
In this process, the main steps were to focus on grouping like terms: terms that have the same variable and terms that are constants. After combining the like terms, you end up with a much simpler expression. The key to simplifying algebraic expressions is always to look for and combine like terms first, which makes solving or graphing the expression easier.