154 +5x > 12x
154 >7 x
22 > x
x<22
Seth would need to rent the court at most 22 times for the membership to be cheaper than a non membership.
Explain if Seth is correct. if he is not correct, explain why by setting up the correct inequality and solve it.
To determine whether Seth's conclusion is correct, we need to understand the context of the membership versus the non-membership cost for renting a court, which is not provided in the initial query. However, we can analyze Seth's mathematical steps to see if his logic in solving the inequality is sound.
From the steps you've provided, it seems that Seth started with the inequality:
154 + 5x > 12x
And then he subtracted 5x from both sides to isolate the term with the variable x:
154 > 7x
Then he divided both sides by 7 to solve for x:
22 > x
or
x < 22
So Seth concluded that x, representing the number of times he would need to rent the court, should be less than 22 for the membership to be cheaper than non-membership.
From a purely algebraic standpoint, Seth's conclusion that x < 22 is correct based on the steps he took to solve the inequality. However, whether this actually means the membership is cheaper depends on the context of the problem, which includes understanding what "154," "5x," and "12x" represent.
In a real-life context, "154" might represent a flat membership fee, while "5x" could represent the cost per court rental with the membership and "12x" the cost per rental without it. If this interpretation is correct, then Seth's conclusion stands that renting the court fewer than 22 times (x < 22) would make the membership the cheaper option.
We can't say definitively whether Seth is correct about the actual cost comparison without additional information. Still, in terms of algebra, his solution to the inequality is correct if the original inequality is accurate.