Question

John, Rasheed, and Jeorge are different ages. Rasheed is six less than twice John’s age. Jeorge’s age is nine more than half of John’s age. The difference between Rasheed and Jeorge’s ages is no more than nine years.1.  Write an expression that represents the difference between Rasheed and Jeorge’s ages.2. Write an absolute value inequality to represent the maximum difference in their ages.3. Determine whether it is possible for John to be twenty years old. Explain your reasoning.4. Algebraically determine the greatest and least age John can be so that the difference between Rasheed and Jeorge’s ages is no more than nine years

Answer 1

Answer: 1) $(2x+6)-(\dfrac{x}{2}-9)$, 2) $x$ 3) No, he should be less than 16 years.

Step-by-step explanation:

Let the age of John be 'x'.

Let the age of Rasheed would be

$2x-6$

Let the age of Jeorge would be

$\dfrac{x}{2}+9$

Difference between Rasheed and Jeorge's age is more than nine years.

$2x-6-(\dfrac{x}{2}+9)$

1) $(2x+6)-(\dfrac{x}{2}-9)$, 2) $x$ 3) No, he should be less than 16 years.