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

Question

50 < 2x + 10 and 2x + 10 < 110

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

x < 20 and x > 50; Malcolm needs to consume less than 20 grams of carbohydrates or more than 50 grams of carbohydrates.
x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.
x > 30 and x < 60; Malcolm needs to consume more than 30 grams of carbohydrates, but less than 60 grams of carbohydrates.
x < 30 and x > 60; Malcolm needs to consume less than 30 grams of carbohydrates or more than 60 grams of carbohydrates.

Answer 1

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

1) 50 < 2x + 10
Subtract 10 from both sides:
40 < 2x
Divide by 2:
20 < x

2) 2x + 10 < 110
Subtract 10 from both sides:
2x < 100
Divide by 2:
x < 50

So, combining the two inequalities, we have:
20 < x < 50

This means Malcolm needs to consume more than 20 grams of carbohydrates but less than 50 grams of carbohydrates. Therefore, the correct answer is:

x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.