Sure, let's go through the process step-by-step for solving the given equation and relate it to the provided steps. Here's how we can fill in each step with the correct operation:
### Given Equation:
[tex]\[
-2(5 x+8)=14+6 x
\][/tex]
### Step-by-Step Solution:
Step 1: [tex]\(-2 \cdot 5x\)[/tex] and [tex]\(-2 \cdot 8\)[/tex]
[tex]\[
-2(5 x + 8) = 14 + 6 x
\][/tex]
Distribute [tex]\(-2\)[/tex] through the parentheses:
[tex]\[
-10 x - 16 = 14 + 6 x
\][/tex]
Process Used: Distribute [tex]\(-2\)[/tex] to [tex]\(5 x\)[/tex] and [tex]\(8\)[/tex].
Drop-down choice for Step 1: Distribute
Step 2: Combine like terms
Combine like terms and move all [tex]\(x\)[/tex] terms to one side:
[tex]\[
-10 x - 16 = 14 + 6 x
\][/tex]
Subtract [tex]\(6 x\)[/tex] from both sides:
[tex]\[
-10 x - 6 x - 16 = 14
\][/tex]
Combine like terms:
[tex]\[
-16 x - 16 = 14
\][/tex]
Process Used: Combine like terms
Drop-down choice for Step 2: Combine like terms
Step 3: Subtract [tex]\(6 x\)[/tex]
Subtracting [tex]\(6 x\)[/tex] from both sides (this repeats part of the previous work but is part of the process):
[tex]\[
-16 x - 16 = 14
\][/tex]
Process Used: Subtract [tex]\(6 x\)[/tex] from both sides
Drop-down choice for Step 3: Subtract [tex]\(6 x\)[/tex]
Step 4: Add
Add [tex]\(16\)[/tex] to both sides:
[tex]\[
-16 x - 16 + 16 = 14 + 16
\][/tex]
Simplifying:
[tex]\[
-16 x = 30
\][/tex]
Process Used: Add [tex]\(16\)[/tex] to both sides
Drop-down choice for Step 4: Add [tex]\(16\)[/tex]. [tex]\(-16\)[/tex].
### Completed Statements:
Step 1: Distribute [tex]\(-2\)[/tex] to [tex]\(5 x\)[/tex] and [tex]\(8\)[/tex].
Step 2: Combine like terms.
Step 3: Subtract [tex]\(6 x\)[/tex].
Step 4: Add [tex]\(16\)[/tex]. [tex]\(-16\)[/tex].
