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how many like terms

-2.1x + 3.7 and 5 + 4.9x

3 answers

To identify the like terms in the expressions \(-2.1x + 3.7\) and \(5 + 4.9x\), we first need to break down the terms in each expression.

From the first expression \(-2.1x + 3.7\):

  • The like terms are \(-2.1x\) (a variable term) and \(3.7\) (a constant term).

From the second expression \(5 + 4.9x\):

  • The like terms are \(4.9x\) (a variable term) and \(5\) (a constant term).

Now, let's identify like terms across both expressions:

  1. The terms with \(x\): \(-2.1x\) from the first expression and \(4.9x\) from the second expression are like terms since they both contain \(x\).
  2. The constant terms: \(3.7\) from the first expression and \(5\) from the second expression are like terms since they are both constants.

In total, you have:

  • 2 like terms with \(x\): \(-2.1x\) and \(4.9x\)
  • 2 like terms that are constants: \(3.7\) and \(5\)

So, there are 2 sets of like terms (1 for variable terms and 1 for constant terms), but if you are counting individual like terms, there are 4 individual terms (2 variable terms and 2 constant terms).

like terms:
_____ 4.9x and 3.7____

It looks like you're trying to identify or arrange the like terms. Here's how it goes:

From the expressions you provided, the terms can be grouped as follows:

  • The terms with the variable \(x\): 4.9x (from the second expression).
  • The constant terms: 3.7 (from the first expression).

However, in the context of identifying like terms, we should note that:

  • 4.9x is a variable term.
  • 3.7 is a constant term.

So, they are not like terms because one contains the variable \(x\) while the other does not.

If you need a format for filling in the blanks, it might look something like this:

  • Like terms: 4.9x and ___ (there are no like terms with 3.7, since it is a different type).

If you have any more specific instructions or further context, please let me know!