Certainly! Let's complete the table step-by-step to determine the number of months ([tex]$x$[/tex]) Katrina needs to save \[tex]$2,600 for a car payment.
\[
\begin{tabular}{c|c}
\hline
Steps & Justification \\
\hline
$[/tex]2,600 = 150x + 50[tex]$ & Given equation \\
\hline
$[/tex]2,600 - 50 = 150x + 50 - 50[tex]$ & Subtract $[/tex]50[tex]$ from both sides to isolate the term with $[/tex]x[tex]$ \\
\hline
$[/tex]2,550 = 150x[tex]$ & Simplification \\
\hline
$[/tex]\frac{2,550}{150} = \frac{150x}{150}[tex]$ & Divide both sides by $[/tex]150[tex]$ to solve for $[/tex]x[tex]$ \\
\hline
$[/tex]x = 17[tex]$ & Simplification \\
\hline
\end{tabular}
\]
Here, we detail the steps to solve the equation given in the problem:
1. Start with the given equation:
\[
2,600 = 150x + 50
\]
2. Subtract 50 from both sides to move the constant term to the left side:
\[
2,600 - 50 = 150x + 50 - 50
\]
3. Simplify both sides:
\[
2,550 = 150x
\]
4. Divide both sides by 150 to isolate $[/tex]x$:
[tex]\[
\frac{2,550}{150} = \frac{150x}{150}
\][/tex]
5. Simplify the division:
[tex]\[
x = 17
\][/tex]
Therefore, Katrina will need 17 months to save enough for the car payment.
