1.3 Solving Linear Equations

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1.3 Solving Linear Equations
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An equation

• Is a statement in which two expressions are
  equal.
• A linear equation in one variable is an equation
  that can be written in the form axcd

A number is a solution of an equation if the
statement is true when the number is substituted
for the variable.
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Two equations are equivalent

• If they have the same solution.
• x 4 1 and x 5 are equivalent because both
  have the number 5 as their only solution.

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The following transformations, or changes,
produce equivalent equations and can be used to
solve an equation.
Add the same number to both sides if ab, then
acbc
Addition Property
Subtract the same number from both sides if ab,
then a-cb-c
Subtraction Property
Multiply both sides by the same non-zero number
if ab, then acbc.
Multiplication Property
Divide both sides by the same non-zero number if
ab, then a/cb/c
Division Property
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Solve an equation with a variable on one side
Write original equation
Subtract 9 from each side
Multiply both sides by 7/3
x 14
Simplify
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Solving an Equation with a Variable on Both Sides.
Write the original equation.
Subtract 5n from each side
Add 9 to both sides.
Finally, divide both sides by 2.
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Using the Distributive Property
Distributive property
Combine like terms.
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Solving an equation with fractions
Write original equation
clear the fractions by multiplying by the LCD
12.
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Assignment 1.3