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Q: 3x plus 8 equals -10x plus x?

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7x + 8 = 10x - 2 ∴ 3x = 10 ∴ x = 10/3

6x - 3x = 5x - 10x + 12 6x - 3x - 5x + 10x = 12 8x = 12 8x/8 = 12/8 x = 12/8 = 3/2 x = 1.5

3x-8=7x+10x 3x-8=17x -8 = 14x -4=7x -4/7

3x2 - 10x - 8 = (3x + 2) (x - 4)

3x² + 10x = 8 Rewrite as: 3x² + 10x - 8 = 0 The only way to get 3x² is 3x and x (3x + -- ) (x + --) The factors of 8 are {1 2 4 8} so the answers must be a pair of them. With 4 factors, and a negative sign (the -8), there are only 8 ways this can be written: (3x + 1)(x - 8) = 3x² - 23x - 8 (3x + 2)(x - 4) = 3x² -10x - 8 (almost) (3x + 4 )(x - 2) = 3x² - 8x - 8 (3x + 8)(x - 1) = 3x² +5x - 8 (3x - 1)(x + 8) = 3x² +23x - 8 (3x - 2)(x + 4) = 3x² + 10x -8 ◄ Success! (3x - 4)(x + 2) = 3x² +2x - 8 (3x - 8)(x + 1) = 3x² -5x - 8 Trial and error, error, error, is the key to this kind of problem. Seeing the -10x early can point you to see that maybe changing the signs can work. ■

y=4x2+3x+8

3x² + 10x = 8 : 3x² + 10x - 8 = 0 Solving for the roots of a quadratic equation gives : x = [-10 ± √(100 + 96)] ÷ 6 = [-10 ± √196] ÷ 6 = [-10 ± 14] ÷ 6 So x = 4/6 = 2/3 and x = -24/6 = -4 x = 2/3 and x = -4

3x+8 = 12 3x = 4 x = 4/3

4x + 5 = 3x + 84x-3x + 5 - 5 = 3x - 3x + 8 -5x = 3

3x2 + 10x - 8 = 0 3x2 + 12x - 2x - 8 = 0 3x(x + 4) - 2(x + 4) = 0 (3x - 2)(x + 4) = 0 So 3x - 2 = 0 or x + 4 = 0 so x = 2/3 or x = -4

3x-6y=-8

-3x + 6 + 15x =11x + 8 ie -3x + 15x - 11x = 8 - 6 ie x = 2

3x + 8 = 2x +28 3x - 2x = 28 - 8 x=20

3x - 8 = 7 so x = 5

70000000y=35t

3x 11 5x=75 x=8

x=-3

3x + 2x = 40 5x = 40 x = 8

-8 + 10x = 18 10x = 18+8 10x = 26 x = 26/10 x = 2.6

(-2, 4)

-3x+2 = 2x-8 8+2 = 2x+3x 10 = 5x x = 2

7x-3=3x+8 7x-3x=8+3 4x=11 x=11/4=2.75

5x+8 = 10x+35x-10x = 3-8-5x = -5x = 1 and by substituting the value of x into the equations y = 13

x=1.6225

3x = x+8 so 3x-x = 8 hence 2x = 8 and so x = 4