 # 1.3 Solving Linear Equations

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1.3 Solving Linear Equations

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.

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.

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

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

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.

Using the Distributive Property
Combine like terms.

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

Assignment 1.3