one particular hotel in the downtown area cost $90 a night. An additional 10% tax is added to the original cost

Equations in mathematics are not always balancing on both sides using a 'equal to' symbol. Sometimes it's a 'not equal to' relationship, as though something is more than or less than the other. In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or any other mathematical expressions.

Inequalities are mathematical expressions that fall within the category of algebra.

Now according to the question-

Total cost spent on hotel stay = cost per night + taxes + parking charges + tips.

As, the paid tax is 10% of the original amount.

The original amount is $90

10% of 90 is = 0.1 × 90

10% tax = $9

Let 'x' be the days spent in hotel.

Then,

The cost spent on stay only is $90x.

The cost spend on tax is $9x.

As, parking is done once only its id added once only.

The total amount spent on tips is $30

Adding all the amount;

90x + 9x + 12 + 30 ≤ 600

On solving,

99x ≤ 558

x ≤ 5.6

As, number can not be in decimals, it could be either 5 day sir 6 days.

Then, total amount spend on days will be-

They would spend $537 if they stayed 5 nights.
They would spend $636 if they stayed 6 nights.

To know more about the inequalities, here

https://brainly.com/question/25275758

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The complete question is-

One particular hotel in the downtown area costs $90 a night. An additional 10% tax is added to the original cost of the hotel room. There is also a one-time $12 for parking charge, and a family can expect to spend $30 on tips during their stay. How many nights can a family spend at the hotel without exceeding their budget of $600.