Fill in the missing work and justification for step 3 when solving [tex]$2(x+1)=10$[/tex].

\begin{tabular}{|l|l|l|}
\hline
Step & Work & Justification \\
\hline
1 & [tex]$2(x+1)=10$[/tex] & Given \\
\hline
2 & [tex]$2x+2=10$[/tex] & Distributive Property \\
\hline
3 & [tex]$2x+2-2=10-2$[/tex] & Subtraction Property of Equality \\
\hline
4 & [tex]$2x=8$[/tex] & Simplify \\
\hline
5 & [tex]$\frac{2x}{2}=\frac{8}{2}$[/tex] & Division Property of Equality \\
\hline
6 & [tex]$x=4$[/tex] & Simplify \\
\hline
\end{tabular}

a. [tex]$2x+2+2=10+2$[/tex]; Addition Property of Equality
b. [tex]$2x+2-2=10-2$[/tex]; Subtraction Property of Equality
c. [tex]$(2x+2)(2)=10(2)$[/tex]; Multiplication Property of Equality
d. [tex]$\frac{2x+2}{2}=\frac{10}{2}$[/tex]; Division Property of Equality



Answer :

Let's fill in the missing work and justification for step 3.

Given: [tex]\( 2(x+1) = 10 \)[/tex]

Step-by-step solution:

1. Step 1: [tex]\( 2(x+1) = 10 \)[/tex] [tex]\( \rightarrow \)[/tex] Given

2. Step 2: [tex]\( 2x + 2 = 10 \)[/tex] [tex]\( \rightarrow \)[/tex] Distributive Property

3. Step 3:
[tex]\[ 2x + 2 - 2 = 10 - 2 \][/tex]
Subtraction Property of Equality: Subtract 2 from both sides to isolate the [tex]\( 2x \)[/tex] term.

4. Step 4: [tex]\( 2x = 8 \)[/tex] [tex]\( \rightarrow \)[/tex] Simplify

5. Step 5:
[tex]\[ \frac{2x}{2} = \frac{8}{2} \][/tex]
[tex]\( \rightarrow \)[/tex] Division Property of Equality: Divide both sides by 2 to solve for [tex]\( x \)[/tex].

6. Step 6: [tex]\( x = 4 \)[/tex] [tex]\( \rightarrow \)[/tex] Simplify

Therefore, for step 3, you should fill in:
[tex]\[ 2x + 2 - 2 = 10 - 2 \quad \text{Subtraction Property of Equality} \][/tex]

So the missing work and justification for step 3:
[tex]\[ 2x + 2 - 2 = 10 - 2 \quad \text{\( \rightarrow \) Subtraction Property of Equality} \][/tex]