Download Prealgebra, Chapter 6 Decimals: 6.6 Solving Equations and

Prealgebra, Chapter 6 Decimals: 6.6 Solving Equations and Problem Solving Objective 1: Solve equations using the addition/subtraction and multiplication/division
principles of equality
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To solve equations with decimals, we treat them exactly like regular
equations
Remember from section 4.3
o Simplify both sides of the equation as needed
ƒ Change subtraction problems into equivalent addition
statements.
ƒ Distribute to get rid of the parenthesis.
ƒ Combine like terms on each side of the equal sign.
o Use the addition/subtraction principle of equality to:
ƒ Get the variables (letter terms) on the left side of the equal
sign by adding the opposite
o Get the constants (numbers) on the right side of the equal sign by
adding the opposite.
o Use the multiplication/division principle of equality to:
ƒ Divide the coefficient (number next to the variable) from
both sides to get the variable by itself.
o The variable is by itself and the number is your answer.
0.3(x – 1.2) = 1.46 – (2.1x + 0.22)
Objective 2: Eliminate decimal numbers from equations using the multiplication
principle
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By using this principle, we can eliminate the decimals from the equation
o First, distribute to clear any parenthesis
o Find the decimal with the most decimal places
o Multiply the entire equation by that place value
o Solve by isolating the variable
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0.3(x – 1.2) = 1.46 – (2.1x + 0.22)
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..
Prealgebra, Chapter 6 Decimals: 6.6 Solving Equations and Problem Solving Objective 3: Solve problems involving one unknown
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Remember your key words so you can translate the problem into an
equation
Review section 4.4
Objective 4: Solve problems using the Pythagorean Theorem
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Right triangle – A triangle that has one right angle
Legs – The sides that form the 90º angle in a right triangle
Hypotenuse – The side directly across from the 90º angle in a right
triangle
The Pythagorean Theorem – Given a right triangle, where “a” and “b”
represent the lengths of the legs and “c” represents the length of the
hypotenuse, then:
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c
3
Objective 5: Solve problems involving two unknowns
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Review sect 4.5 for solving problems with 2 unknowns
o Determine which unknown will be represented by a variable
ƒ Let the unknown that is being acted ON be the variable
o Use one of the relationships to describe the other unknown(s) in
terms of the variable
o Use the other relationship to write an equation
o Solve the equation
Resource: Carson, T. (2009 ). Prealgebra – 3rd ed..