Download Section 2.2 day 1

Section 2.2
Day 1
A) Algebraic Properties of Equality
• Let a, b, and c be real numbers:
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1)
2)
3)
4)
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5) Reflexive Property – For any real number a, a = a
6) Symmetric Property – If a = b, then b = a
7) Transitive Property – If a = b and b = c, then a = c
8) Substitution Property – If a = b, then a can be substituted for b in any
equation or expression.
Addition Property – If a = b, then a + c = b + c
Subtraction Property – If a = b, the a - c = b – c
Multiplication Property – If a = b, the ac = bc
Division Property – If a = b, and c ≠ 0, then a ÷ c = b ÷ c
Use them
when we did
Equation
Solving.
• 9) Distributive Property – a(b + c) = ab + ac or a(b – c) = ab - ac
• Ex. 1 Solve 3x + 12 = 8x – 18 and write a
reason for each step.
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3x + 12 = 8x – 18
• 3x – 3x + 12 = 8x – 3x - 18
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12 = 5x – 18
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12 + 18 = 5x – 18 + 18
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30 = 5x
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5
5
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x=6
given
Subtraction property of equality
Addition property of equality
Division property of equality
• Student practice:
• Justify each step in solving the equation, in a
two column proof.
• 1)
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3x + 2 = 17
2x  5
4)
3
5
2(3x – 5) = 50
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5) 1 x  2  2 x  1
3
5
2
y
• 3) 3y + 4 =
5
• 2)