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questionamy is eight years older than twice her cousin alicia’s age. the sum of their ages is less than 32.let x represent alicia's age.which inequality represents alicia’s possible age?

Answer :

An inequality that represents Alicia’s possible age is x < 8.

For given question,

let x represent Alicia's age.

Amy is eight years older than twice her cousin Alicia’s age.

So, Amy's age would be 2x + 8

The sum of their ages is less than 32.

We write above statement in mathematical expression.

sum of their ages = (2x + 8) + x

                             = 3x + 8

The sum of their ages is less than 32.

We use the symbol < for 'less than'

So, the mathematical expression form of given statement would be,

(3x + 8) < 32

So, we get an inequality 3x + 8 < 32

⇒ 3x < 32 - 8

⇒ 3x < 24

⇒ x < 24/3

⇒ x < 8

Therefore, an inequality that represents Alicia’s possible age is x < 8.

Learn more about an inequality here:

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