Question

Fill in the blanks!

What is the sum of the algebraic expressions -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

Let's go through the steps to find the sum of the algebraic expressions -2.1x + 3.7 and 5 + 4.9x.

1. **Identify like terms.**
- Like terms: **-2.1x** and **4.9x**
- And **3.7** and **5**

2. **Rewrite using properties of operations when necessary.**
- Combine the like terms:
\[
-2.1x + 4.9x + 3.7 + 5
\]

3. **Simplify.**
- Combine the x terms:
\[
(-2.1 + 4.9)x = 2.8x
\]
- Combine the constant terms:
\[
3.7 + 5 = 8.7
\]
- Therefore, the simplified expression is:
\[
2.8x + 8.7
\]

4. **Check by substituting a value for x.**
- For example, 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 original expressions:
\[
1.6 + 9.9 = 11.5
\]
- Using the simplified expression:
\[
2.8(1) + 8.7 = 2.8 + 8.7 = 11.5
\]

Thus, the sum of the algebraic expressions is confirmed, and we filled in the blanks as follows:

1. **-2.1x and 4.9x; 3.7 and 5**
2. **(as shown above)**
3. **2.8x + 8.7**
4. **substituting a value for x**