1. Writing Algebraic Expressions
Objective:
Be able to write an algebraic expression for a word phrase or write a word phrase for an expression.

2. Warm Up ) 7x + 4 for x = 6 2.) 8y – 22 for y = 9 46
Evaluate each algebraic expression for the given value of the variables.
) 7x + 4 for x = 6
2.) 8y – 22 for y = 9
3.) 12x + for x = 7 and y = 4
4.) y + 3z for y = 5 and z = 6 46 50 8 y 86 23

3. Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua.
An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.
When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

4. Notes
In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.

5. Addition Phrases: More than Increase by Greater than Add Total Plus
Sum

6. Subtraction Phrases: Decreased by Difference between Take Away Less
Less than*
Subtract from*

7. Multiplication Phrases:
Product
Times
Multiply Of
Twice or double
Triple

8. Notes
Division expressions should be written using the fraction bar instead of the traditional division sign.

9. Examples: Translate Verbal Phrases into Expressions.
less than quantity 6 times a number n n – 4
2. 3 times the sum of 7 and a number y ( 7+y )
3. The difference of 22 and the square of a number x – x2

10. The product of 8 and the quantity 6 plus a.
Board Drill
Translate it mathematical expression
The product of 8 and the quantity 6 plus a.

11. Twice the product of a and b.
Board Drill
Twice the product of a and b.

12. Board Drill
Subtract 8 from b

13. Board Drill
x less than 10

14. The difference of x and y
Board Drill
The difference of x and y

15. thrice the difference of a and b
Board Drill
thrice the difference of a and b

16. Seatwork 1.Twice the number b.
Write the following verbal phrases into mathematical expressions.
1.Twice the number b.
2. The product of 9 and the quantity x plus y.
3. Twice the difference of m and n.
4. The sum of a and 2 divided by x
5. 4 subtracted from the product of 8 and n.

17. Write Equations and Inequalities
Equation – a mathematical sentence formed by placing the symbol “ = ” between two expressions.
Inequality – a mathematical sentence formed by placing one of the symbols <, <, or >, > between two expressions.

18. is greater than or equal to
Key Concept
Symbol
Meaning
Associated Word =
is equal to
the same as
< 
is less than
fewer than
is less than or
equal to
at most
no more than
> 
is greater than
more than
is greater than or equal to
at least
no less than

19. Note: Combining Inequalities.
Sometimes two inequalities are combined. For example, the inequalities x > 4 and x < 9 can be combined to form the inequality 4 < x < 9, which is read as “ x is greater than 4 and less than 9.”

20. Write the following into mathematical equations or inequalities.
The difference of twice a number and 8 is 12.
Answer: 2k – 8 = 12
2. The product of 6 and a number n is at least 24.
Answer: 6n > 24
3. The sum of thrice a number m and is at most 32.
Answer: 3m + 10 < 32

21. Twice the product of x any y is equal to 23
Board Drill
Twice the product of x any y is equal to 23

22. 6 the quantity 5 plus x is greater than or equal to 9.
Board Drill
6 the quantity 5 plus x is greater than or equal to 9.

23. Board Drill
2 times x minus 5 is at most 3

24. 7 the quantity x plus c is at least 245
Board Drill
7 the quantity x plus c is at least 245

25. Board Drill
x is greater than 10 and less than 7

26. The sum of x and y is at most 8 and no more than 9
Board Drill
The sum of x and y is at most 8 and no more than 9

27. Seatwork
Translate the verbal phrases into mathematical equations and inequalities. 6. Twice the product of a and b is equal to the quantity m plus n is greater than the quantity c minus d is at least times the difference of x and y is Thrice the product of x and y is less than or equal to 5.

28. Homework Review for a quiz tomorrow. a. Evaluate Expressions.
b. Order of Operations
c. Write Expressions, Equations, and Inequalities.
Answer page 24 (UBD Book)
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