Question

What is the sum of the algebraic expression -2.1x + 3.7 and 5 + 4.9x?

1. _ like terms.
like terms:
_ 4.9x and 3.7 _

2. Rewrite using properties of operations when necessary.
3. Simplify
4. Check by _ .

Answer 1

To find the sum of the algebraic expression \(-2.1x + 3.7\) and \(5 + 4.9x\), let's follow the steps outlined:

1. **Identify Like Terms**
- Like terms in this expression are:
- For the \(x\) terms: \(-2.1x\) and \(4.9x\)
- For the constant terms: \(3.7\) and \(5\)

2. **Rewrite Using Properties of Operations When Necessary**
- We can write the two expressions together:
\[
(-2.1x + 3.7) + (5 + 4.9x)
\]

3. **Simplify**
- Combine the like terms:
- For the \(x\) terms:
\[
-2.1x + 4.9x = (4.9 - 2.1)x = 2.8x
\]
- For the constant terms:
\[
3.7 + 5 = 8.7
\]
- Putting it all together, we have:
\[
2.8x + 8.7
\]

4. **Check by Substituting Values**
- To check our work, we can substitute a specific value for \(x\) and verify that both original expressions yield the same result as the simplified expression:
- Let’s substitute \(x = 1\):
- Original expressions:
\[
-2.1(1) + 3.7 = -2.1 + 3.7 = 1.6
\]
\[
5 + 4.9(1) = 5 + 4.9 = 9.9
\]
- Sum of the original:
\[
1.6 + 9.9 = 11.5
\]
- Simplified expression:
\[
2.8(1) + 8.7 = 2.8 + 8.7 = 11.5
\]
- Since we got the same result, our simplification is verified.

The final answer is:
\[
2.8x + 8.7
\]