Transcript Lesson 1-3

Five-Minute Check (over Lesson 1–2)
Then/Now
New Vocabulary
Example 1: Verbal to Algebraic Expression
Example 2: Algebraic to Verbal Sentence
Key Concept: Properties of Equality
Example 3: Identify Properties of Equality
Key Concept: Addition and Subtraction / Multiplication and
Division Properties of Equality
Example 4: Solve One-Step Equations
Example 5: Solve a Multi-Step Equation
Example 6: Solve for a Variable
Example 7: Standardized Test Example
Over Lesson 1–2
A. naturals (N), wholes (W),
integers (Z)
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B
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D. naturals (N), wholes (W),
integers (Z), rationals (Q),
reals (R)
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B
C
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C. naturals (N), wholes (W),
rationals (Q), reals (R)
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B.
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B. wholes (W), integers (Z),
reals (R)
Over Lesson 1–2
A. naturals (N), wholes (W)
B. reals (R)
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B
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D. integers (Z), reals (R)
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B.
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D.
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C. rationals (Q), reals (R)
Over Lesson 1–2
Name the property illustrated by
a + (7 + c) = (a + 7) + c.
A. Associative Property
of Addition
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B
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D. Commutative Property
of Addition
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C. Substitution Property
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B. Distributive Property
Over Lesson 1–2
Name the property illustrated by
3(4 + 0.2) = 3(4) + 3(.02).
A. Associative Property
of Addition
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B
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D. Substitution Property
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C. Distributive Property
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B. Identity Property
Over Lesson 1–2
Simplify (2c)(3d) + c + 5cd + 3c2.
A. 3c2 + 5cd + c
B. 3c2 + 11cd + c
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B
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D. 3c2 + c
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C. 3c2 + 10cd
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Over Lesson 1–2
Which equation illustrates the Additive Identity
Property?
A. 5 + 0 = 5
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C. 5 + (–5) = 0
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B. 5(1) = 5
You used properties of real numbers to
evaluate expressions.
• Translate verbal expressions into algebraic
expressions and equations, and vice versa.
• Solve equations using the properties of
equality.
• open sentence
• equation
• solution
Verbal to Algebraic Expression
A. Write an algebraic expression to represent the
verbal expression 7 less than a number.
Answer: n – 7
Verbal to Algebraic Expression
B. Write an algebraic expression to represent the
verbal expression the square of a number
decreased by the product of 5 and the number.
Answer: x2 – 5x
A. Write an algebraic expression to represent the
verbal expression 6 more than a number.
A. 6x
B. x + 6
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B
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D. x – 6
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C. x6
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B. Write an algebraic expression to represent the
verbal expression 2 less than the cube of a number.
A. x3 – 2
B. 2x3
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B
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D. 2 + x3
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C. x2 – 2
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Algebraic to Verbal Sentence
A. Write a verbal sentence to represent 6 = –5 + x.
Answer: Six is equal to –5 plus a number.
Algebraic to Verbal Sentence
B. Write a verbal sentence to represent 7y – 2 = 19.
Answer: Seven times a number minus 2 is 19.
A. What is a verbal sentence that represents the
equation n – 3 = 7?
A. The difference of a number
and 3 is 7.
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D. The difference of a number
and 7 is 3.
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C. The difference of 3 and a
number is 7.
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B. The sum of a number and
3 is 7.
B. What is a verbal sentence that represents the
equation 5 = 2 + x?
A. Five is equal to the difference
of 2 and a number.
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B
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D. Five is equal to the sum of
2 and a number.
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C. Five is equal to the quotient
of 2 and a number.
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B. Five is equal to twice a
number.
Identify Properties of Equality
A. Name the property illustrated by the statement.
a – 2.03 = a – 2.03.
Answer: Reflexive Property of Equality
Identify Properties of Equality
B. Name the property illustrated by the statement.
If 9 = x, then x = 9.
Answer: Symmetric Property of Equality
A. What property is illustrated by the statement?
If x + 4 = 3, then 3 = x + 4.
A. Reflexive Property of
Equality
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D. Substitution Property of
Equality
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C. Transitive Property of
Equality
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B. Symmetric Property of
Equality
B. What property is illustrated by the statement?
If 3 = x and x = y, then 3 = y.
A. Reflexive Property of
Equality
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D. Substitution Property of
Equality
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C. Transitive Property of
Equality
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B. Symmetric Property of
Equality
Solve One-Step Equations
A. Solve m – 5.48 = 0.02. Check your solution.
m – 5.48 = 0.02
Original equation
m – 5.48 + 5.48 = 0.02 + 5.48
Add 5.48 to each
side.
m = 5.5
Check m – 5.48 = 0.02
?
5.5 – 5.48 = 0.02
0.02 = 0.02 
Answer: The solution is 5.5.
Simplify.
Original equation
Substitute 5.5 for m.
Simplify.
Solve One-Step Equations
Original equation
Simplify.
Solve One-Step Equations
Check
Original equation
?
Substitute 36 for t.

Simplify.
Answer: The solution is 36.
A. What is the solution to the equation x + 5 = 3?
A. –8
B. –2
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D. 8
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C. 2
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B. What is the solution to the equation
A. 5
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D. 30
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C. 15
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Solve a Multi-Step Equation
Solve 53 = 3(y – 2) – 2(3y – 1).
53 = 3(y – 2) – 2(3y – 1)
Original equation
53 = 3y – 6 – 6y + 2
Apply the Distributive
Property.
53 = –3y – 4
Simplify the right side.
57 = –3y
Add 4 to each side.
–19 = y
Divide each side by –3.
Answer: The solution is –19.
What is the solution to 25 = 3(2x + 2) – 5(2x + 1)?
A. –6
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D. 6
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Solve for a Variable
Area formula
Subtract πr 2 from
each side.
Simplify.
Solve for a Variable
Divide each side
by πr.
Simplify.
GEOMETRY The formula for the perimeter of a
rectangle is
where P is the perimeter,
and w is the width of the rectangle.
What is this formula solved for w?
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Read the Test Item
You are asked to find the value of the expression 4g – 2.
Your first thought might be to find the value of g and then
evaluate the expression using this value. Notice that you
are not required to find the value of g. Instead, you can
use the Subtraction Property of Equality.
Solve the Test Item
Original equation
Subtract 7 from each side.
Simplify.
Answer: C
If 2x + 6 = –3, what is the value of 2x – 3?
A. 12
B. 6
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D. –12
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C. –6
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