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.

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

Step-by-step explanation:

1. 110<2x+10

First, switch sides.

2x+10>110

Then, subtract by 10 both sides of equation.

2x+10-10>110-10

Simplify.

110-10=100

2x>100

Divide by 2 both sides of equation.

2x/2>100/2

Simplify, to find the answer.

100/2=50

x>50

x>50 is the correct answer.

2. 2x+10<310

First, you subtract by 10 from both sides of equation.

2x+10-10<310-10

Then, simplify.

310-10=300

2x<300

Divide by 2 from both sides of equation.

2x/2<300/2

Simplify, to find the answer.

300/2=150

x<150

x<150 is the correct answer.

A. the first option is the correct answer.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.