המורה שלך ברשת

משוואות

משוואה ליניארית

$ 3x - 2 = 3- 2x ~~~~~~ (x = 1) $
$ -x + 14 = 2 - 2x ~~~~~~ (x=-12)$
$ 3x = x + 4 + 2x ~~~~~~ (no ~~ solution) $
$ x - 3 = \frac{3}{2} - 2x ~~~~~~ (x=1.5) $
$ \frac{x}{4} - \frac{1}{3} = - 2x ~~~~~~ (x = \frac{4}{27}) $
$ - \frac{5}{4} = \frac{3}{4} x - \frac{x}{3} ~~~~~~ (x=-3) $
$ \frac{3}{2}x - \frac{2}{3} = \frac{3}{4} - 7x ~~~~~~ (x=\frac{17}{92}) $
$ \frac{3}{2}x + 2= \frac{1}{2}x + 2 ~~~~~~ (Every ~~ x) $

משוואות ריבועיות

$ x^2 + 4x + 3 = 0 ~~~~~~ (x_1 = -1, x_2 = -3) $
$ x^2 + 7x + 6 = 0 ~~~~~~ (x_1 = -6, x_2 = -1)$
$ x^2 + 6x + 8 = 0 ~~~~~~ (x_1=-2, x_2 = -4) $
$ 2x^2 + 3x - 6 = x^2 + 4x ~~~~~~ (x_1=-2, x_2 = 3) $
$ x^2 -4 = 0 ~~~~~~ (x_1 = 2, x_2 = -2) $
$ x^2 - 36 = 0 ~~~~~~ (x_1=6, x_2 = -6) $
$ x^2 + 1 = 0 ~~~~~~ (no ~~ solution) $
$ x^2 -3x = 0 ~~~~~~ (x_1 = 0, x_2 = 3) $
$ 4x^2 - 2x = 0 ~~~~~~ ( x_1 = 0 ~~,~~ x_2 = 0.5 ) $

משוואות עם שורשים

$ \sqrt{x^2 + 16} = 5 ~~~~~~ (x_1 = -3, x_2 = 3) $
$ \sqrt{2x + 1} = -\sqrt{x} ~~~~~~ (no ~~ solution)$
$ \sqrt{x^2} + \sqrt{x} = 0 ~~~~~~ (x = 0) $
$ x = -\sqrt{x+2} ~~~~~~ (x = -1) $

משוואות עם שברים

$ \frac{1}{x^2 - x} = \frac{1}{2x} + \frac{1}{x^2} ~~~~~~ (x_1 = -1, x_2 = 2) $
$ \frac{1}{x + 3} - \frac{1}{2x + 6} = \frac{x - 1}{2x - 6} ~~~~~~ (x_1 = -1, x_2 = 0)$
$ \frac{x}{x^2-2x-24} + \frac{1}{6-x} = \frac{1}{x+4} ~~~~~~ (x = 2 ) $
$ \frac{x-1}{2(9-x^2)} + \frac{2}{3 - x} = 1 ~~~~~~ (x_1 = -3.5, x_2 = 1 ) $
$ \frac{x-8}{12 - 3x^2} + \frac{2}{2+x} = 1 ~~~~~~ (x_1 = \frac{8}{3}, x_2 = -1 ) $

משוואות עם ערך מוחלט

$ |x-1| = 8 ~~~~~~ (x_1 = 9, x_2 = -7) $
$ |x + 2| - 2x = 4 ~~~~~~ (x=-2)$
$ |x + 4| + |x| = 2 ~~~~~~ (no ~~ solution) $
$ |x + 4| + |x| = 8 ~~~~~~ (x_1 = 2, x_2 = -6 ) $

מערכת משוואות

$ x + y = 8 $
$ x - y = 8 ~~~~~~ (x = 8, ~ y = 0)$
$ 2x + y = 8 $
$ -4x - 2y = -16 ~~~~~~ (Every ~~ Point ~~ s.t (x, 8-2x) )$
$ 4x - y = -2 $
$ 2x + 4y = 26 ~~~~~~ (x = 1, ~ y = 6)$
$ 4x + 8y = 8 $
$ 2x + 4y = 12 ~~~~~~ (no ~~ solution)$
$ x^2 + y^2 = 1 $
$ 2y + 4x = 4 ~~~~~~ ((x_1,y_1)=(1,0) ~~ (x_2, y_2) = (0.6, 0.8))$