Transcript 2.4 Notes Beginning Algebra

Chapter 2
Solving
Linear
Equations
and
Inequalities
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© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-1
2-1
1
Chapter Sections
2.1 – Combining Like Terms
2.2 – The Addition Property of Equality
2.3 – The Multiplication Property of Equality
2.4 – Solving Linear Equations with a Variable on
Only One Side of the Equation
2.5 – Solving Linear Equations with the Variable on
Both Sides of the Equation
2.6 – Formulas
2.7 – Ratios and Proportions
2.8 – Inequalities in One Variable
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-2
2-2
2
Solving Linear
Equations with a
Variable on Only One
Side of the Equation
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-3
2-3
3
Equations with a Variable on One Side
1.
2.
3.
4.
5.
6.
If the equation contains fractions, multiply both sides
by the LCD to eliminate fractions.
Use the distributive property to remove parentheses.
Combine like terms on the same side of the equation.
Use the addition property to obtain an equation with
the term containing the variable on one side of the
equation and a constant on the other side. This will
result in an equation of the form ax = b.
Use the multiplication property to isolate the
variable.
Check the solution in the original equation.
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-4
2-4
4
Solving Equations
Example: Solve the equation 5x – 7 = 13
5x -7 + 7 = 13 + 7
(Add 7 to both sides)
5x = 20
5
5
(Divide both sides by 5)
x=4
Don’t forget to check!
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-5
2-5
5
Solving Equations Containing Decimal
Numbers or Fractions
Example: Solve the equation x + 1.24 – 0.07x = 4.96
0.93x + 1.24 = 4.96 (Like terms were combined)
0.93x + 1.24 - 1.24 = 4.96 – 1.24 (Subtract 1.24
from both sides)
0.93x = 3.72
0.93x = 3.72
0.93
0.93 (Divide both sides by 0.93)
x=4
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-6
2-6
6
Helpful Hints and Definitions



To evaluate an expression means to find its
numerical value.
To simplify an expression means to perform
operations and combine like terms.
To solve an equation means to find the value or the
values of the variable that make the equation a true
statement.
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-7
2-7
7