Example #1 
Sue and David are friends.  David is 6 years older than Sue.
If the sum of Sue and David's age is less than 42 years, what is the greatest age each can be?

When translating, you must begin with a "let" statement.
In a let statement you assign a variable to stand for the
quantity (ies) you are trying to solve for.
In this problem there are two quantities we are interested in finding.
That's right...Sue's age and David's age.....

Let x = Sue's age
Let x+6 = David's age
Now for the translation into an algebraic inequality:
(x) + (x + 6) < 42
 

Example #2
On a farm, the number of cows is 50 more than twice the number of sheep.  If there are at most 250 animals in all, find the greatest number of cows, and the greatest number of sheep there could be on this farm.
(Do you understand that that means the total number
of animals must be less than or equal to 250)

let x = the number of sheep
let 2x+ 50 = the number of cows
(x) + (2x+50) ≤ 250
 

Example #3
Bob received grades of 88, 91, 89, and 87 on four science tests. 
What is the lowest grade that Bob can receive on the fifth test
in order for his average to be greater than 90?
(Remember to find an average add up all the terms and divide by the number of terms)
Let x = the grade he must receive on the fifth test
(88 + 91 + 89 + 87 + x) ÷ 5 > 90
 

Example #4
In Sara's bank, there are twice as many nickels as quarters. 
If the value of these coins is at least $8.00, find the smallest possible number of nickels and quarters in her bank.

Let x = the number of quarters
Let 2x = the number of nickels
Then 25x = the value of the quarters in cents
Then 10x = the value of the nickels in cents
10x + 25x ≥ 800
(remember $8 = 800 cents!)