Question

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

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

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

Answer 1

Answer:

The correct option is 2.

Step-by-step explanation:

The given inequalities are

$50$             .... (1)

$2x+10$            .... (2)

Solve each inequality.

Subtract 10 from each side of inequality (1).

$50-10$

$40$

Divide both the sides by 2.

$20$

The value of x is more than 20.

Subtract 10 from each side of inequality (2).

$2x+10-10$

$2x$

Divide both the sides by 2.

$x$

The value of x is less than 50.

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

Hence the correct option is 2.