A.5Solving Equations Ex. 1Solve.6(x - 1) + 4 = 7x + 1 x = -3 Ex. 2Multiply each term by the LCD -----> 12 4x + 9x = 24 13x = 24.

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A.5Solving Equations Ex. 1Solve.6(x - 1) + 4 = 7x + 1 x = -3 Ex. 2Multiply each term by the LCD -----> 12 4x + 9x = 24 13x = 24

Ex. 3An equation with an Extraneous Solution Again, mult. Each term by the LCD. x + 2 = 3(x - 2) - 6x x + 2 = 3x x 4x = -8 x = -2 But, x = -2 yields a den. of zero, therefore there are no solutions.

Ex. 4Solving a Quadratic by Factoring A. 6x 2 = 3xFirst, take the 3x to the other side and then factor. 6x 2 - 3x = 0 3x(2x - 1) = 0Set both factors = to 0. 3x = 0 x = 0 2x - 1 = 0 2x = 1 x = 1/2 B. 9x 2 - 6x + 1 = 0First, factor. (3x -1)(3x - 1) = 0Set = to 0 and solve.

Ex. 5Solving quadratic equations. A. 4x 2 = 12 x 2 = 3 B. (x - 2) 2 = 5 Ex. 6aCompleting the Square x 2 - 6x + 2 = 0 First, take 2 to the other side. x 2 - 6x = -2 To complete the square take half the x-term and square it. Add it to both sides. x 2 - 6x = (x - 3) 2 = 7

Ex. 6bCompleting the Square when the leading coefficient is not 1 Divide each term by 3. Take 5/3 to the other side. Now, complete the square. Take the square root of both sides. Day 1 stop

Ex. 7Use the Quadratic Formula to solve x 2 + 3x - 9 = 0

Ex. 8Solve by factoring. x 4 - 3x = 0 Factor (x 2 - 2)(x 2 - 1) = 0 Set both factors = 0 or factor again. x = 0 x 2 = 2 x = 0 x 2 = 1

Ex. 9Solve by grouping. x 3 - 3x 2 - 3x + 9 = 0 x 2 (x - 3) - 3(x - 3) = 0 Factor out an (x - 3) (x - 3)(x 2 - 3) = 0 x = 3

Ex. 10 Solving a Radical Isolate the radical. Now square both sides. 2x + 7 = x 2 + 4x = x 2 + 2x - 3Factor or use quad. formula 0 = (x + 3)(x - 1) Possible answers for x are - 3 and 1. Check them in the original equation to see if they work. Only x = 1 works!

Ex. 11 An equation Involving Two Radicals Isolate the more complicated rad. Square both sides. Once again, isolate the radical. Square both sides. x 2 + 2x + 1 = 4(x + 4) x 2 - 2x - 15 = 0 (x - 5)(x + 3) = 0 Only x = 5 works.

Ex. 12Solving an Equation Involving Absolute Value Split into 2 equations. x 2 - 3x = -4x + 6x 2 - 3x = 4x -6Now solve them for x. x 2 + x - 6 = 0 (x + 3)(x - 2) = 0 x 2 - 7x + 6 = 0 (x - 1)(x - 6) = 0 Possible answers are -3, 2, 1, and 6. Which ones work? -3 and 1