Sect. 1.3 Solving Equations

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Sect. 1.3 Solving Equations
Goal 1 Translate verbal expressions into
equations. Goal 2 Solve equations using
properties of equality
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Verbal expressions to Algebraic expressions
Verbal expressions can be translated into
mathematical expressions using the language of
Algebra.
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Write an Algebraic expression to represent each
verbal expression
a) Three more than a number
X 3
b) Six times the cube of a number
6x3
c) The square of a number decreased by the
product of 5 and the number.
X2 5x
d) Twice the difference of a number and 6.
2(x 6)
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Properties of Equality

• Reflexive Property a a
• x 21 x - 21

• Symmetric Property If a b, then b a
• If x 9 14, then 14 x 9

• Transitive Property If a b and b c, then a
  c
• If x n 1, and n 1 11, then x 11

• Substitution Property If a b, then a may be
  replaced by b and b may be replaced by a.
• If (2 3)x 18, then 5x 18

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• Addition Property of Equality (APOE)
• If a b, then a c b c
• If x 4 11, then x 15

• Subtraction Property of Equality (SPOE)
• If a b, then a c b c
• If x 9 23, then x 14

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Name the property illustrated by each statement
a) If xy 28 and x 7, then 7y 28
Substitution Property
b) A 2.13 A 2.13
Reflexive Property
c) If x 11 y, then 11 y x
Symmetric Property
d) If x 9 41, then x 32
SPOE
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Solving One-Step Equations
Solve. Check your solution N 5.48 0.02
N 5.5
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Solve and Check
t 36
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Solve and Check.
X -16
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Solving a Multi-step equation.
53 3(y 2) 2(3y 1)
y - 19
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Solving for a Variable
The formula for the Area of a trapezoid is
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To solve a word Problem
1. Define a variable
2. Write an equation
3. Solve by applying the properties of equality
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Define a variable, write an equation, Solve, and
Check
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Carl wants to replace the five windows in the
bedrooms of his house. His neighbor Will is a
carpenter and will install them for 250. If
Carl has budgeted 1000 for the total cost, what
is the maximum amount he can spend on each window.
Let x amount spent for each window
Equation 5x 250 1000
Cost of each window is 150