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

a

Explanation:

Answer 2

Option A (x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates).

Explanation:

There are two inequalities. One is 110 < 2x + 10 and 2x + 10 < 310. x is the amount of carbs consumed in grams, the first inequality is the lower limit, and the second inequality is the upper limit. The question requires to solve the two inequalities.

1)

110 < 2x + 10.

100 < 2x.

50 < x (or x > 50).

2)

2x + 10 < 310.

2x < 300.

x < 150.

Now combining the two inequality gives:

50 < x < 150.

So Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates. Therefore, Option A is the correct answer!!!