An entertainment firm offers several DJ choices and light shows that range in price based on the rental time period.

The DJ's cost between $219.00 and $369.00 per night and the light shows cost between $159.00 and $309.00 per night.

If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay, x.

MUST SHOW VALID WORK :)

If you're looking to book both a DJ and a light show we have to take into account the minimum that you'll pay up to the maximum cost "x". This can be done by adding the lowest cost for both meaning:

$219 + $159 = $378

And the most you'll pay:

$369 + $309 = $678

So you can say that the amount you'll pay is in between $378 and $678. Mathematically speaking you can also say that you'll pay more than or equal to $378 and less than or equal to $678. The previous statement can be written mathematically as a compound inequality as such:

[tex]378\leq x\leq 678[/tex]