The value of x is: x=7/8. Work: 5x-3=4-3x +3 +3 ________ 5x=7-3x +3x +3x ________ 8x=7 /8 /8 ________ x=7/8
2(3x + 4) = 6x + 8 3(x - 5) = 3x - 15 6x + 8 - 3x + 15 = 3x + 23
No, it has an infinite number of solutions. The coordinates of each and every point on the line 3x + 2y + 4 = 0 is a solution.
2(3x + 4) = 6x + 8 3(x - 5) = 3x - 15 6x + 8 - 3x + 15 = 3x + 23
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x + 2) - 4(x + 2) = (x + 2)(3x - 4).
x-3x = -8 -2x = -8 x = 4
If: 3x+8-x = 5x-4 Then: x = 4
x=4 or x=-4
3x2-2x-8 = (3x+4)(x-2) when factored
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. ■
3x = x+8 so 3x-x = 8 hence 2x = 8 and so x = 4
The value of x is: x=7/8. Work: 5x-3=4-3x +3 +3 ________ 5x=7-3x +3x +3x ________ 8x=7 /8 /8 ________ x=7/8
3x + x + 8 = 204x + 8 = 204x = 12x = 3
3x+8 = 12 3x = 4 x = 4/3
2(3x + 4) = 6x + 8 3(x - 5) = 3x - 15 6x + 8 - 3x + 15 = 3x + 23
3x + 8 = 20 3x = 20 - 8 3x = 12 3x = 12/3 x = 4
3(x-4)