Question

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

Answer 1

Option 3 - x > 225 and x < 325; Ashlynn needs to consume more than 225 grams of carbohydrates, but less than 325 grams of carbohydrates.

Explanation:

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:

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

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

Solution :

Solving the inequalities,
`460 < 2x + 10` ....(1)

Subtract 10 both side,

`460-10 < 2x + 10-10`

`450< 2x`

Divide by 2 both side,

`(450)/(2)<(2x)/(2)`

`225<x`

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

Solving the inequalities,
`2x + 10 < 660` ....(2)

Subtract 10 both side,

`2x + 10-10 < 660-10`

`2x< 650`

Divide by 2 both side,

`(2x)/(2)<(650)/(2)`

`x<325`

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.

Answer 2

C. x > 225 and x < 325

Explanation:

Simplify each inequality:

460 < 2x + 10 =>

450 < 2x

225 < x

x > 225

and

2x + 10 < 660 =>

2x < 650

x < 325

So x > 225 and x < 325.