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Given the taxable income amount of [tex] \$57,360 [/tex], express the tax table line that would be used in interval notation:

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\multicolumn{2}{|l|}{\text{If line 43 (taxable income) is -}} & \multicolumn{4}{|c|}{\text{And you are -}} \\
\hline
\text{At least} & \text{But less than} & \text{Single} & \text{Married filing jointly} & \text{Married filing separately} & \text{Head of a household} \\
\hline
57,000 & 57,050 & 10,050 & 7,631 & 10,050 & 8,579 \\
\hline
57,050 & 57,100 & 10,063 & 7,639 & 10,063 & 8,591 \\
\hline
57,100 & 57,150 & 10,075 & 7,646 & 10,075 & 8,604 \\
\hline
57,150 & 57,200 & 10,088 & 7,654 & 10,088 & 8,616 \\
\hline
57,200 & 57,250 & 10,100 & 7,661 & 10,100 & 8,629 \\
\hline
57,250 & 57,300 & 10,113 & 7,669 & 10,113 & 8,641 \\
\hline
57,300 & 57,350 & 10,125 & 7,676 & 10,125 & 8,654 \\
\hline
57,350 & 57,400 & 10,138 & 7,684 & 10,138 & 8,666 \\
\hline
57,400 & 57,450 & 10,150 & 7,691 & 10,150 & 8,679 \\
\hline
57,450 & 57,500 & 10,163 & 7,699 & 10,163 & 8,691 \\
\hline
57,500 & 57,550 & 10,175 & 7,706 & 10,175 & 8,704 \\
\hline
57,550 & 57,600 & 10,188 & 7,714 & 10,188 & 8,716 \\
\hline
57,600 & 57,650 & 10,200 & 7,721 & 10,200 & 8,729 \\
\hline
57,650 & 57,700 & 10,212 & 7,730 & 10,212 & 8,741 \\
\hline
\end{array}
\]

Taxable income of [tex] \$57,360 [/tex] falls in the interval: [tex] (57,350, 57,400) [/tex].

Answer :

To solve this problem, we need to figure out which tax bracket the given taxable income of \[tex]$57,360 falls into, using the specified interval notation from the tax table provided.

1. Identify the Taxable Income Range:
- First, look at the given taxable income, which is \$[/tex]57,360.

2. Analyze the Tax Table:
- The tax table is divided into intervals, each with a lower bound and an upper bound. It lists the starting point and the ending point for each tax bracket.

3. Find the Correct Interval:
- We need to locate the interval where the taxable income \[tex]$57,360 falls into. By examining the intervals closely:
- The intervals start from (57,000 to 57,050), (57,050 to 57,100) and so forth.
- Continue through the intervals until you find where \$[/tex]57,360 fits.

4. Interval Identification:
- Check the boundaries of each interval one by one. The objective is to find one where the lower bound is less than or equal to \[tex]$57,360 and the upper bound is more than \$[/tex]57,360.
- Finally, when you reach the interval (57,350, 57,400), you can see that \[tex]$57,360 is within this range. Specifically, \$[/tex]57,360 falls between \[tex]$57,350 and \$[/tex]57,400.

Therefore, the taxable income of \$57,360 is in the interval (57,350, 57,400). So, this is the interval notation for the tax bracket that applies to the given taxable income.

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