Fill in the blanks!

Question

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

1. Identify like terms.
2. Rewrite using properties of operations when necessary.
-2.1x + 3.7 + 5 + 4.9 x

Commutative property
-2.1x + _ + 5 + 3.7

Distributive property
x (_ + 4.9) + 5 + 3.7

3. Simplify
2.8x + _

4. Check by substitution.
x = 1
-2.1 (1) + 3.7
-2.1 + 3.7 = _
2.8 (1) + 8.7
= _
5 + 4.9 (1)
5 + 4.9 = _
9.9 + 1.6 = 11.5

Our correct expression, 2.8x + 8.7, is the sum of the two algebraic expressions.

Answer 1

Let's go through each step of your prompt.

1. Identify like terms. The like terms in the expression \(-2.1x + 3.7 + 5 + 4.9x\) are:

   • \( -2.1x\) and \( 4.9x\) (these are the terms with \(x\))
   • \(3.7\) and \(5\) (these are the constant terms)

2. Rewrite using properties of operations when necessary. We can rearrange it using the commutative property: \[ -2.1x + 4.9x + 3.7 + 5 \] Applying the distributive property is unnecessary here, but we can prepare it as follows: \[ (-2.1 + 4.9)x + (3.7 + 5) \]

3. Simplify. Simplify the coefficients: \[ (-2.1 + 4.9)x = 2.8x \] And for the constant terms: \[ (3.7 + 5) = 8.7 \] So now we combine them to give: \[ 2.8x + 8.7 \]

4. Check by substitution. Let's evaluate both forms with \(x = 1\).

   • For the original expression: \[ -2.1(1) + 3.7 = -2.1 + 3.7 = 1.6 \] \[ 5 + 4.9(1) = 5 + 4.9 = 9.9 \] Sum: \[ 1.6 + 9.9 = 11.5 \]

   • For the simplified expression: \[ 2.8(1) + 8.7 = 2.8 + 8.7 = 11.5 \]

Since both calculations yield \(11.5\), the original expression and the simplified expression are equivalent.

Thus, the correct expression is indeed: \[ \boxed{2.8x + 8.7} \]

Answer 2

You didn't fill in the blanks

Answer 3

Apologies for not filling in the blanks clearly! Let’s go through your prompt again and fill in each of the provided blanks step-by-step.

1. Identify like terms.
The expression is:
\(-2.1x + 3.7 + 5 + 4.9x\)
Like terms are:

• \( -2.1x\) and \( 4.9x\) (terms with \(x\))
• \(3.7\) and \(5\) (constant terms)

2. Rewrite using properties of operations when necessary.
Original expression:
\(-2.1x + 3.7 + 5 + 4.9x\)

Using the Commutative Property:
Starting with the like terms, \(-2.1x + 4.9x + 3.7 + 5\)

Distributive Property:
\(-2.1x + 4.9x\) can be grouped:
\[ x(-2.1 + 4.9) + (3.7 + 5) \]

So, we can fill in the blank as: \[ x( _ + 4.9) + 5 + 3.7 \] The blank is \( -2.1 \).

3. Simplify.
Now, simplifying:

• Combine the coefficients: \(-2.1 + 4.9 = 2.8\)
• Combine the constants:
  \(3.7 + 5 = 8.7\)

Thus the final expression is: \[ 2.8x + 8.7 \] This means you'll fill in the blank as: \[ 2.8x + _ \] The blank is \( 8.7 \).

4. Check by substitution. When \(x = 1\):

• From the original expression:
  \[ -2.1(1) + 3.7 = -2.1 + 3.7 = 1.6 \] \[ 5 + 4.9(1) = 5 + 4.9 = 9.9 \] Total: \[ 1.6 + 9.9 = 11.5 \]

• From the simplified expression:
  \[ 2.8(1) + 8.7 = 2.8 + 8.7 = 11.5 \]

Both calculations confirm that the sums are correct.

So, here’s the partially filled prompt:

1. Identify like terms.

   • Blank (like terms for constants): 3.7 + 5

2. Rewrite using properties of operations when necessary.
   Using the Commutative property: \(-2.1x + 4.9 + 5 + 3.7\)
   Using the Distributive property:
   \(x(-2.1 + 4.9) + 5 + 3.7\)

3. Simplify:

   • \(2.8x + 8.7\)

I hope this format meets your expectations better! Thank you for your patience!

Answer 4

You still haven't filled in these blanks:

4. Check by substitution.
x = 1
-2.1 (1) + 3.7
-2.1 + 3.7 = _
2.8 (1) + 8.7
= _
5 + 4.9 (1)
5 + 4.9 = _
9.9 + 1.6 = 11.5

Answer 5

Thank you for your clarification! Let’s fill in the blanks step by step for the substitution check.

4. Check by substitution.

For \( x = 1 \):

1. Calculate the original expression: \[ -2.1(1) + 3.7 \] \[ -2.1 + 3.7 = 1.6 \quad \text{(This fills in the first blank)} \]

2. Calculate the simplified expression: \[ 2.8(1) + 8.7 \] \[ 2.8 + 8.7 = 11.5 \quad \text{(This fills in the second blank)} \]

3. Calculate the second part of the original expression: \[ 5 + 4.9(1) \] \[ 5 + 4.9 = 9.9 \quad \text{(This fills in the third blank)} \]

4. Add the results from the first part and the second part of the original expression: \[ 9.9 + 1.6 = 11.5 \]

So here are the filled-in blanks:

Check by substitution:

• \( -2.1(1) + 3.7 \)
  \( -2.1 + 3.7 = 1.6 \)

• \( 2.8(1) + 8.7 \)
  \( = 11.5 \)

• \( 5 + 4.9(1) \)
  \( 5 + 4.9 = 9.9 \)

Thank you again for your patience! I hope this completes it as intended!