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

Compound inequality combines multiple single inequalities.

The solution and interpretation of the inequality is:

$x > 50$ and $x < 150$.  Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.

We have:

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

Solve for x in both inequalities

$110 < 2x + 10$

$110 -10 < 2x$

$100 < 2x$

Divide both sides by 2

$50 < x$

Rewrite as:

$x > 50$

Also, we have:

$2x + 10< 310$

$2x< 310 - 10$

$2x< 300$

Divide by 2

$x < 150$

So, the solutions to the inequalities are:

$x > 50$ and $x < 150$

This means that Ryan needs to consume more than 50 but less than 150 grams of carbohydrates.

Hence, (a) is correct

Read more about compound inequalities at:

https://brainly.com/question/13290962