How do you solve this 4x – 2x -20x + x
The Correct Answer and Explanation is:
Expression:
4x−2x−20x+x4x – 2x – 20x + x4x−2x−20x+x
Step-by-step Simplification:
- Combine like terms (all terms involve x): (4x−2x−20x+x)(4x – 2x – 20x + x)(4x−2x−20x+x)
- Do the operations from left to right:
- 4x−2x=2x4x – 2x = 2x4x−2x=2x
- 2x−20x=−18x2x – 20x = -18x2x−20x=−18x
- −18x+x=−17x-18x + x = -17x−18x+x=−17x
Final Answer:
−17x\boxed{-17x}−17x
Explanation:
To solve an algebraic expression like 4x−2x−20x+x4x – 2x – 20x + x4x−2x−20x+x, we need to simplify by combining like terms. “Like terms” are terms that have the same variable raised to the same power. In this case, all terms contain the variable x and no exponents, which means they are all like terms.
The key to simplifying such expressions is to treat the coefficients (the numbers in front of the variable) as if they are simple numbers and perform the basic operations: addition and subtraction.
Here’s how it works step-by-step:
- Start with the first two terms: 4x−2x=2x4x – 2x = 2x4x−2x=2x. This is because 4 minus 2 equals 2, and the variable x is common.
- Next, subtract 20x from 2x: 2x−20x=−18x2x – 20x = -18x2x−20x=−18x. Again, we subtract the coefficients and keep the variable.
- Finally, add x to -18x. Remember, x is the same as 1x, so −18x+1x=−17x-18x + 1x = -17x−18x+1x=−17x.
The entire process is like balancing a checkbook with x’s—add and subtract the amounts represented by each x term.
This expression doesn’t have any constants (just numbers with no variable), so we don’t need to worry about those.
In conclusion, when you combine all the like terms, you get a simplified expression of:−17x\boxed{-17x}−17x
This is the simplest form and the correct final answer.
