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1 Section 1.10 Solving Equations

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2 Three Types of Equations 1._____________________: True only for certain values of the variable. 2.____________________: True for ALL values of the variable. 3.____________________: Not true for any values.

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3 Guidelines for solving linear equations 1.Use the distributive property to remove all parentheses. 2.Simplify each side of the equation separately by combining like terms. 3.Use inverse operations to get the variable on one side of the equation, constants on the other. 4.Use inverse operations to solve for (isolate) the variable. 5.Check answers in original equation.

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4 Equations Involving Numerical Fractions To eliminate fractions, multiply both sides of the equation by the least common denominator (LCD).

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5 Solving Proportions Use cross-multiplication.

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Application #1 The combined electrical resistance (R) of R 1 and R 2 connected in parallel is given by If the combined resistance is 30 and R 2 = 75 , find R 1. 6

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Application #2 Lens equation: where f = lens focal length p = distance of object from lens q = distance of image from lens Given a focal length of 50 mm. To focus an object 1 m away, what must be the distance of the image from the lens (to the nearest mm)? 7

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8 Solving Absolute Value Equations

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1 Warm Up 3 Points Total 1 for each Solve and check: 7x – 2 = 4x 2) 7(5x – 2) = 6(6x – 1) 3) 3x – 3 = 5(x – 4)

1 Warm Up 3 Points Total 1 for each Solve and check: 7x – 2 = 4x 2) 7(5x – 2) = 6(6x – 1) 3) 3x – 3 = 5(x – 4)

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