Questionlect the expressions that are equivalent to $(-5 k+3)+(6 k+3)$ $\begin{array}{c} (6 k+3)+(-5 k+3) \\ 6 k+3+-5 k+3 \\ -5 k+6 k+6 \end{array}$ $k+6$

Studdy Solution

STEP 1

1. We are given an expression and need to determine which of the provided options are equivalent to it.
2. The expression is $(-5k + 3) + (6k + 3)$ .
3. We will simplify the expression and compare it to the given options.

STEP 2

1. Simplify the original expression.
2. Compare the simplified expression to each option.
3. Determine which options are equivalent.

STEP 3

Simplify the original expression $(-5k + 3) + (6k + 3)$ .
Combine like terms: - Combine the terms with $k$ : $-5k + 6k$ . - Combine the constant terms: $3 + 3$ .

STEP 4

Calculate the combined terms: - $-5k + 6k = 1k$ or simply $k$ . - $3 + 3 = 6$ .
Thus, the simplified expression is: $k + 6$

STEP 5

Compare the simplified expression $k + 6$ to each option:
1. $(6k + 3) + (-5k + 3)$ : - Rearranging terms does not change the sum, so this is equivalent.
2. $6k + 3 + -5k + 3$ : - This is the same as the original expression, so it is equivalent.
3. $-5k + 6k + 6$ : - Simplifying this gives $k + 6$ , so it is equivalent.
4. $k + 6$ : - This is exactly the simplified expression, so it is equivalent.
The expressions that are equivalent to $(-5k + 3) + (6k + 3)$ are:
1. $(6k + 3) + (-5k + 3)$
2. $6k + 3 + -5k + 3$
3. $-5k + 6k + 6$
4. $k + 6$

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