Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations...

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Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases to algebraic expressions. Identify solutions of equations. Identify solutions of equations from a set of numbers. Distinguish between expressions and equations. Objectives

Transcript of Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations...

Page 1: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Variables, Expressions, and Equations

Evaluate algebraic expressions, given values for the variable.

Translate word phrases to algebraic expressions.

Identify solutions of equations.

Identify solutions of equations from a set of numbers.

Distinguish between expressions and equations.

Objectives

Page 2: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

CONCEPTS

• Variable: A symbol, usually a letter, that represents one or more numbers.

• An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operation.

Page 3: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

First, replace the variables with their values.

Then find the value of the numerical

expression using the order of operation.

if

Objective 1 Evaluate algebraic expressions, given

values for the variable.

Page 4: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Example 2-4a

Evaluate

Replace x with 4, y with 3 and z with 2.

Evaluate.

Subtract 16 and 3.

Multiply 2 and 13.

Evaluate .

Add. Answer:

Objective 1 Evaluate algebraic expressions, given

values for the variable.

Page 5: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Evaluate .

Example 2-4b

Answer: 28

Page 6: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

• Addition: sum, plus, more than, increased by.

• Subtraction: difference, less, less than, subtract, minus,

decreased by. • Multiplication: times, product,

• multiply, of, twice.

• Division: quotient, divided.

Objective 2 Translate word phrases to algebraic expressions.

Page 7: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Eight more than a number x

Eight more than a number x

8 + x

Objective 2 Translate word phrases to algebraic expressions.

Fifty eight less a number x

58 - x

Fifty eight less a number x

Page 8: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Example 1-1a

Five less than a number c.

The words less than suggest subtraction.

a number c less five

c – 5

Answer: Thus, the algebraic expression is .

Objective 2 Translate word phrases to algebraic expressions.

Page 9: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Eight times number x

The word times suggests multiplication.

Answer: 8x

.

Objective 2 Translate word phrases to algebraic expressions.

the quotient of a number n and 5

The word quotient suggests division.

Answer:

.

Page 10: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Objective 2 Translate word phrases to algebraic expressions.

Two thirds of the original volume v.

Answer:

The word of implies multiply.

The sum of 9 and 2 times the number d.

Answer: .

Sum implies add, and times implies multiply.

Page 11: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

7 less the product of 4 and a number x

7 – 4x

7 less than 3 times a number x

What is 6 more than 2 times

a certain number x?

four times the sum of x and y

four times the quantity x plus y

Objective 2 Translate word phrases to algebraic expressions.

Page 12: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Example 1-1d

Write an algebraic expression for each

verbal expression.

a. nine more than a number h

b. the difference of 6 and 4 times a

number x

c. one half the size of the original

perimeter p

Answer:

Answer:

Answer:

Page 13: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

one-half the cube of n

two-thirds the square of a number

one- fourth 8 times g cubed

Objective 2 Translate word phrases to algebraic expressions.

Page 14: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Objective 3 Identify solutions of equations.

An equation is a statement that two algebraic expressions are equal. An equation always includes the equality symbol =

A solution of an equation containing a variable that makes the equation true

Page 15: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

State whether the equation is true or false

for the given value of the variable.

Substitute 3 into the

equation for the

variable x and solve. True when x = 3

Substitute 7 into the

equation for the

variable x and solve. False when x = 7

Objective 3 Identify solutions of equations.

Page 16: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Find the solution or solutions for the equation for the given

replacement set.

Substitute each value in the replacement

set for the variable x.

False when x = 5 True when x = 6 False when x = 7

Objective 4 Identify solutions of equations from a set

of numbers.

Page 17: Variables, Expressions, and Equations€¦ · 26/8/2014  · Variables, Expressions, and Equations Evaluate algebraic expressions, given values for the variable. Translate word phrases

Objective 5 Distinguish between expressions and

equations.

Left side = Right side

Equation (solve for x)

Expression

To simplify or evaluate