Ashlynn is trying a low-carbohydrate diet. She would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:

460 < 2x + 10 and 2x + 10 < 660

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

x > 235 and x < 335; Ashlynn needs to consume more than 235 grams of carbohydrates, but less than 335 grams of carbohydrates.
x < 235 and x > 335; Ashlynn needs to consume less than 235 grams of carbohydrates or more than 335 grams of carbohydrates.
x > 225 and x < 325; Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.
x < 225 and x > 325; Ashlynn needs to consume less than 225 grams of carbohydrates or more than 325 grams of carbohydrates.

please help

Given : Ashlynn is trying a low-carbohydrate diet. She would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:

[tex]460 < 2x + 10[/tex] and [tex]2x + 10 < 660[/tex]

To find : Solve for x in the inequality, and explain what the answer represents?

Solution :

Solving the inequalities, [tex]460 < 2x + 10[/tex] ....(1)

Subtract 10 both side,

[tex]460-10 < 2x + 10-10[/tex]

[tex]450< 2x[/tex]

Divide by 2 both side,

[tex]\frac{450}{2}<\frac{2x}{2}[/tex]

[tex]225<x[/tex]

i.e. The value of x is more than 225.

Solving the inequalities, [tex]2x + 10 < 660[/tex] ....(2)

Subtract 10 both side,

[tex]2x + 10-10 < 660-10[/tex]

[tex]2x< 650[/tex]

Divide by 2 both side,

[tex]\frac{2x}{2}<\frac{650}{2}[/tex]

[tex]x<325[/tex]

i.e. The value of x is less than 325.

As, x > 225 and x < 325; Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.

Therefore, Option 3 is correct.