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

Question

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: \[ 2.8x + 8.7 \]