Question

Select all pairs of like terms in the expression 2x - 6 + 5x + 3.

A. 2x and -6
B. -6 and 3
C. 2x and 5x
D. 3x and 3

Answer 1

To identify the pairs of like terms in the expression \(2x - 6 + 5x + 3\), we should first clarify what like terms are. Like terms have the same variable raised to the same power.

Now, let's break down the expression:

- The terms are \(2x\), \(-6\), \(5x\), and \(3\).
- \(2x\) and \(5x\) are like terms because they both contain the variable \(x\).
- \(-6\) and \(3\) are constant terms but are not considered like terms with \(x\).

Now we can analyze the options:

A. \(2x\) and \(-6\) - NOT a pair of like terms, different types
B. \(-6\) and \(3\) - NOT a pair of like terms, both constants but not related
C. \(2x\) and \(5x\) - YES, a pair of like terms
D. \(3x\) and \(3\) - NOT a pair of like terms, \(3x\) is not in the original expression

Thus, the only pair of like terms is:

**C. \(2x\) and \(5x\)**.