A restaurant owner needs to order at least 176 filet mignon steaks to be stocked for a busy Friday night. He only has room to store 321 steaks in his refrigerator. Model the number of steaks the restaurant owner can order, using a compound inequality.
x ≥ 176 and x ≤ 321
x ≤ 176 and x ≥ 321
x ≤ 176 and x ≤ 321
x ≥ 176 and x ≥ 321
x ≥ 176 and x ≤ 321
Ashlynn is trying a low-carbohydrate diet. She would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
460 < 2x + 10 and 2x + 10 < 660
Solve for x in the inequality, and explain what the answer represents.
x > 235 and x < 335; Ashlynn needs to consume more than 235 grams of carbohydrates, but less than 335 grams of carbohydrates.
x < 235 and x > 335; Ashlynn needs to consume less than 235 grams of carbohydrates or more than 335 grams of carbohydrates.
x > 225 and x < 325; Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.
x < 225 and x > 325; Ashlynn needs to consume less than 225 grams of carbohydrates or more than 325 grams of carbohydrates.
x > 225 and x < 325; Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.
To solve for x, we first need to isolate the variable in the inequality. We do this by subtracting 10 from both sides of the compound inequality:
460 < 2x + 10 < 660
450 < 2x < 650
Then, we divide by 2 to get the value of x:
225 < x < 325
So, Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.
The correct compound inequality to model the number of steaks the restaurant owner can order is:
x ≥ 176 and x ≤ 321
To model the number of steaks the restaurant owner can order using a compound inequality, we need to consider two conditions:
1. The restaurant owner needs to order at least 176 filet mignon steaks.
2. The restaurant owner can only store a maximum of 321 steaks in his refrigerator.
To express these conditions as a compound inequality, we use the logical operator "and" to connect the two conditions.
The first condition states that the number of steaks ordered should be at least 176. We can represent this as "x ≥ 176".
The second condition states that the number of steaks ordered should be less than or equal to 321. We can represent this as "x ≤ 321".
Combining these two conditions using the logical operator "and", the compound inequality is:
x ≥ 176 and x ≤ 321
Therefore, the correct answer is: x ≥ 176 and x ≤ 321.