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Published bySibyl Charity Stevenson Modified over 5 years ago

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1.1 Linear Equations A linear equation in one variable is equivalent to an equation of the form To solve an equation means to find all the solutions of the equation.

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Equivalent Equations Two or more equations that have precisely the same solutions are called equivalent equations. Examples of equivalent equations:

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**Solving a Linear Equation**

Solve the equation: We replace the original equation by succession of equivalent equations. Add 5 to both sides. Simplify. Divide both sides by 3.

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**Solving a Linear Equation Involving Fractions**

Multiply both sides by the least common denominator 30. Be sure to multiply all terms by 30. Divide out common factors. Subtract 5x to get the x-terms on the left. Simplify. Solve the equation:

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**Solve an Equation Involving Rational Expressions**

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**This is the given equation.**

Multiply both sides by 5x (LCD). Be sure to multiply all terms by 5x. Divide out the common factors. Simplify. Subtract 4 from both sides. Divide both sides by 2.

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