To solve the equation [tex]\(3x - 2 = 4\)[/tex], we follow these steps with corresponding reasons:
1. Given: The initial equation is [tex]\(3x - 2 = 4\)[/tex].
2. Addition Property of Equality: To isolate the term involving [tex]\(x\)[/tex], we add 2 to both sides of the equation:
[tex]\[
3x - 2 + 2 = 4 + 2
\][/tex]
Simplifying this, we get:
[tex]\[
3x = 6
\][/tex]
3. Division Property of Equality: To solve for [tex]\(x\)[/tex], we divide both sides of the equation by 3:
[tex]\[
\frac{3x}{3} = \frac{6}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
x = 2
\][/tex]
So, the completed table along with the reasons would look like this:
[tex]\[
\begin{array}{c|c}
\text{Step} & \text{Reason} \\
\hline
3x - 2 = 4 & \text{Given} \\
3x = 6 & \text{Addition Property of Equality} \\
x = 2 & \text{Division Property of Equality} \\
\end{array}
\][/tex]
Each step ensured that we maintained the equality while isolating [tex]\(x\)[/tex] and solving the equation.
