To find the number of cars [tex]\( x \)[/tex] Mr. Schwartz builds before placing an order for more wheels, start with the initial supply of 85 wheels and note that he uses 4 wheels per car. He plans to order more wheels once he has fewer than 40 wheels left.
The inequality representing this situation can be written as:
[tex]\[ 85 - 4x < 40 \][/tex]
To solve for [tex]\( x \)[/tex], rearrange the inequality:
[tex]\[ 85 - 40 < 4x \][/tex]
[tex]\[ 45 < 4x \][/tex]
Divide by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[ \frac{45}{4} < x \][/tex]
[tex]\[ 11.25 < x \][/tex]
Since [tex]\( x \)[/tex] must be an integer (you can't build a fraction of a car), round 11.25 up to the next whole number:
[tex]\[ x = 12 \][/tex]
Therefore, Mr. Schwartz will need to order more wheels after building 12 cars.
Thus, your answer should be:
The inequality that can be used to find the number of cars, [tex]\( x \)[/tex], Mr. Schwartz builds before he places an order for more wheels is [tex]\( 85 - 4x < 40 \)[/tex].
Mr. Schwartz will need to order more wheels after building 12 cars.
