8
3x + x + 8 = 204x + 8 = 204x = 12x = 3
3x = 2 x 9 2 x 9 = 18 3x = 18 18/x = 6 Therefore, x = 6
Let the number be x: 2(2x+4) = 3x+4 4x+8 = 3x+4 4x-3x = 4-8 x = -4
3x^2 + 10x + 8 = (3x + 4)(x + 2)
It is an open sentence. 3x = 3 x X 2y = 2 x Y, If 8 is the product then: x = 4 and y = 2. 3 x 4 = 12 2 x 2 = 4 12- 4 = 8
3x-2=x+8 (+2) 3x=x+10 (-x) 2x=10 (/2) x=5
8
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. ■
If you mean: y = x+4 and y = 3x+8 then x = -2 and y = 2
3x + x + 8 = 204x + 8 = 204x = 12x = 3
2(3x + 4) = 6x + 8 3(x - 5) = 3x - 15 6x + 8 - 3x + 15 = 3x + 23
The product of (3x-1)(x+5) = 3x^2 +14x -5 by multiply out the brackets
6x + 6 = 3x - 2 Bring 3x to the left and subtract: 6x - 3x = 3x 3x + 6 = -2 -2 - 6 = -8 -8 / 3 X = -8/3
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x+2) - 4(x+2) = (3x-4)*(x+2)
-3x+2 = 2x-8 8+2 = 2x+3x 10 = 5x x = 2
If you mean: 3x+2 = 8 then x = 2