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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
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.
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.
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.
Evaluate .
Example 2-4b
Answer: 28
• 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.
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
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.
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:
.
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.
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.
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:
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.
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
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.
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.
Objective 5 Distinguish between expressions and
equations.
Left side = Right side
Equation (solve for x)
Expression
To simplify or evaluate
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