Sure, let's go through the steps given the context of solving the equation [tex]\(2(x+1) = 10\)[/tex].
\begin{tabular}{|l|l|l|}
\hline
Step & Work & \multicolumn{1}{|c|}{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}
Let's explain the step-by-step solution:
- Step 1: Given
The equation we start with is given as [tex]\(2(x+1) = 10\)[/tex].
- Step 2: Distributive Property
Apply the distributive property to the left-hand side of the equation, expanding the expression as follows:
[tex]\[
2(x+1) = 2 \cdot x + 2 \cdot 1 = 2x + 2
\][/tex]
So, we have [tex]\(2x + 2 = 10\)[/tex].
- Step 3: Subtraction Property of Equality
To isolate the term containing [tex]\(x\)[/tex] on one side, we need to get rid of the constant term [tex]\(2\)[/tex]. We do this by subtracting [tex]\(2\)[/tex] from both sides of the equation:
[tex]\[
2x + 2 - 2 = 10 - 2
\][/tex]
Thus, the equation simplifies to:
[tex]\[
2x = 8
\][/tex]
- Step 4: Simplify
After subtracting [tex]\(2\)[/tex] from both sides, we have [tex]\(2x = 8\)[/tex].
- Step 5: Division Property of Equality
To solve for [tex]\(x\)[/tex], we divide both sides of the equation by [tex]\(2\)[/tex]:
[tex]\[
\frac{2x}{2} = \frac{8}{2}
\][/tex]
This simplifies to:
[tex]\[
x = 4
\][/tex]
- Step 6: Simplify
The last step confirms the solution:
[tex]\[
x = 4
\][/tex]
Therefore, the missing work and justification for Step 3 are [tex]\(2x + 2 - 2 = 10 - 2\)[/tex]; Subtraction Property of Equality.
