Simplify -2k+6+3k-2-k

Solution:

Step:1 Combine like terms by adding $-2k$ to $3k$. Resulting in $k+6-2-k$.

Step:2 Eliminate the similar terms in the expression $k+6-2-k$.

Step:2.1 Cancel out $k$ with $-k$ to get $0+6-2$.

Step:2.2 Combine $0$ and $6$ to simplify to $6-2$.

Step:3 Deduct $2$ from $6$ to obtain the final result, which is $4$.

Knowledge Notes:

To simplify an algebraic expression, you follow these steps:

1. Combine like terms: Like terms are terms that contain the same variable raised to the same power. In this case, $-2k$ and $3k$ are like terms, and so are $k$ and $-k$.

2. Use the distributive property if necessary: The distributive property states that $a(b+c)=ab+ac$. This is not used in this problem, but it's a common step in simplifying expressions.

3. Cancel out terms: If you have a term and its opposite, they cancel each other out. In this problem, $k$ and $-k$ cancel each other out.

4. Perform arithmetic operations: Once like terms are combined and opposites are canceled, you perform the remaining arithmetic operations, such as addition and subtraction.

In this problem, the expression $-2k+6+3k-2-k$ is simplified by combining like terms and performing arithmetic operations. The terms involving $k$ cancel each other out, leaving a simple arithmetic problem of $6-2$, which equals $4$.