Define a variable and write an inequality for each of the following.

A. When 3 times a number is decreased by 8, the result is at least 2 times the number.

B. Ignatz, the Airedale, and Angus, the Scottie, collect bones. Ignatz has 5 more than Angus. They have at least 27 bones between them. What is the least each dog has collected?

C. John is 10 years older than Kathy and the sum of their ages is more than 60. Kathy is older than what age?

If the number is x, then 3x-8 is=or greater than 2x.

Agnus has x bones and Ignatz has x+5.
Then x+x+5=27 or 2x=27-5=22
Or x=11. Ignatz has 11+5=16.

Kathy mis x and John is x+10
Then x+x+10 is greater than 60
Or 2x+10is greater than 60
Or 2x 10 is greater than 50
Or x is greater than 25.

PS: There is slight typo.

Please readt first line as 'Kath is' and third line as 2x+10.

A. To define a variable and write an inequality for the given situation, let's assume that the number is represented by the variable "x".

The equation "3 times a number is decreased by 8" can be written as "3x - 8". The phrase "at least 2 times the number" can be written as "2x" or "2 times x".

Putting it all together, the inequality statement becomes:
3x - 8 ≥ 2x

B. To define a variable and write an inequality for this situation, let's assume the number of bones collected by Ignatz is represented by the variable "I", and the number of bones collected by Angus is represented by the variable "A".

According to the information given, Ignatz has 5 more bones than Angus. So, the inequality can be written as:
I = A + 5

The statement "They have at least 27 bones between them" can be written as:
I + A ≥ 27

Combining both equations, we get:
(A + 5) + A ≥ 27

C. To define a variable and write an inequality for this scenario, let's assume the age of Kathy is represented by the variable "K" and the age of John is represented by the variable "J".

The information given states that "John is 10 years older than Kathy." This can be written as:
J = K + 10

The statement "the sum of their ages is more than 60" can be written as:
J + K > 60

Combining both equations, we get:
(K + 10) + K > 60

Now we can solve these inequalities to find the values that satisfy them.