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

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

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.

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

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

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

Multiplication Phrases: Product Times Multiply Of Twice or double Triple

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

Examples: Translate Verbal Phrases into Expressions. 1. 4 less than quantity 6 times a number n. 6n – 4 2. 3 times the sum of 7 and a number y. 3( 7+y ) 3. The difference of 22 and the square of a number x 22 – x2

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.

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

Board Drill Subtract 8 from b

Board Drill x less than 10

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

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

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.

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.

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

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.”

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 10 is at most 32. Answer: 3m + 10 < 32

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

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.

Board Drill 2 times x minus 5 is at most 3

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

Board Drill x is greater than 10 and less than 7

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

Seatwork Translate the verbal phrases into mathematical equations and inequalities. 6. Twice the product of a and b is equal to 7. 7. 3 the quantity m plus n is greater than 8. 8. 5 the quantity c minus d is at least 4. 9. 7 times the difference of x and y is 23. 10. Thrice the product of x and y is less than or equal to 5.

Homework Review for a quiz tomorrow. a. Evaluate Expressions. b. Order of Operations c. Write Expressions, Equations, and Inequalities. Answer page 24 (UBD Book) Items 2 to 11