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]
