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1.3 Solving Linear Equations

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1 1.3 Solving Linear Equations

2 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 ax+c=d A number is a solution of an equation if the statement is true when the number is substituted for the variable.

3 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.

4 The following transformations, or changes, produce equivalent equations and can be used to solve an equation. Add the same number to both sides: if a=b, then a+c=b+c Addition Property Subtract the same number from both sides: if a=b, then a-c=b-c Subtraction Property Multiply both sides by the same non-zero number: if a=b, then ac=bc. Multiplication Property Divide both sides by the same non-zero number: if a=b, then a/c=b/c Division Property

5 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

6 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.

7 Using the Distributive Property
Combine like terms.

8 Solving an equation with fractions
Write original equation “clear” the fractions by multiplying by the LCD 12.

9 Assignment 1.3

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