Final answer:
To solve the compound inequality for Malcolm's carbohydrate intake on a low-carb diet, each part of the inequality was solved individually. The result showed that Malcolm should consume between 20 to 50 grams of carbs (excluding the extra 10 grams) per serving to stay within his diet's carb limit.
Step-by-step explanation:
Malcolm is trying to determine the amount of carbohydrates he can consume while on a low-carbohydrate diet, which is expressed as a compound inequality. The inequality is given as 50 < 2x + 10 and 2x + 10 < 110. To solve for x, we will solve each part of the compound inequality separately.
For the first part of the inequality 50 < 2x + 10, we subtract 10 from both sides to get 40 < 2x and then divide both sides by 2, resulting in 20 < x.
For the second part of the inequality 2x + 10 < 110, we subtract 10 from both sides to get 2x < 100, and divide by 2 to get x < 50.
Combining both results, we find that the value of x must satisfy 20 < x < 50. Therefore, Malcolm can consume between 20 to 50 grams of carbs two times the value of x, plus an extra 10 grams, in order to stay within his diet's carb limit.