To complete the given steps and justifications for solving the equation [tex]\( y = 770 - 55x \)[/tex], let’s do it step-by-step with appropriate justifications:
1. Given:
[tex]\[
y = 770 - 55x
\][/tex]
This is the initial equation provided.
2. Subtract 770 from both sides (subtraction property of equality):
[tex]\[
y - 770 = 770 - 55x - 770
\][/tex]
Here we are isolating the term involving [tex]\( x \)[/tex] by moving the constant term on the right side to the left side.
3. Simplification:
[tex]\[
y - 770 = -55x
\][/tex]
After subtracting 770 from both sides, we simplify the right-hand side.
4. Divide both sides by -55 (division property of equality):
[tex]\[
\frac{y - 770}{-55} = \frac{-55x}{-55}
\][/tex]
To isolate [tex]\( x \)[/tex], we divide both sides of the equation by -55.
5. Simplification:
[tex]\[
x = \frac{y - 770}{-55}
\][/tex]
This is the final simplified form, where [tex]\( x \)[/tex] is isolated.
Putting it all together in the table:
[tex]\[
\begin{tabular}{|c|l|}
\hline Steps & Justification \\
\hline y=770-55x & given \\
\hline y-770=770-55x-770 & subtraction property of equality \\
\hline y - 770 = -55x & simplification \\
\hline \frac{y-770}{-55}=\frac{-55x}{-55} & division property of equality \\
\hline x = \frac{y-770}{-55} & simplification \\
\hline
\end{tabular}
\][/tex]
This organized sequence of steps and justifications shows how to solve the given linear equation for [tex]\( x \)[/tex].
