Question

Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:

110 < 2x + 10 and 2x + 10 < 310

Solve for x in this inequality, and explain what the answer represents.

x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
x < 50 and x > 150; Ryan needs to consume less than 50 grams of carbohydrates or more than 150 grams of carbohydrates.
x > 60 and x < 160; Ryan needs to consume more than 60 grams of carbohydrates, but less than 160 grams of carbohydrates.
x < 60 and x > 160; Ryan needs to consume less than 60 grams of carbohydrates or more than 160 grams of carbohydrates.

Answer 1

To solve the compound inequality, we first solve each part separately:

110 < 2x + 10
Subtracting 10 from both sides:
100 < 2x
Dividing by 2:
50 < x

2x + 10 < 310
Subtracting 10 from both sides:
2x < 300
Dividing by 2:
x < 150

Combining the two inequalities, we get:
50 < x < 150

Therefore, Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates. The correct answer is:
x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.