Macejova Matika

a $$(4 - 5x) * 2 - 7(x + 4) + 2x <= 0$$ $$8 - 10x - 7x - 28 + 2x <= 0$$ $$-15x - 20 <= 0$$ $$-15x <= 20$$ $$-3x <= 4$$ $$x <= -4/3$$

d

<m>2*4x-5_3_-_5x_2_x_1_6_m_m_8x-10_3-_5x_2_x_1_6_m_m_16x-20-15x_x_1_m_m_x-20_x_1_m_m_-20_1_m_nerovnice_nema_reseni_----_g_m_4_7x-_8-x_2_14_x_2_2_7_-1_-2_2_0_m_m_4x_7-_64-16x_x_2_14_x_2_2_1_7_4_0_m_m_8x_14_-64_16x-x_2_14_x_2_14_-4_m_m_8x-64_16x-x_2_x_2_-56_m_m_24x-64_-56_m_m_24x_8_m_m_x_8_24_m_m_x_1_3_m_rovnice_s_neznamou_ve_jmenovateli_zadani_m_3x_7_x-5_-_5_x_x*3-{25-3x}/{x^2-5x}=0</m>

<m>x<>5</m> <m>x<>0</m>

<m>{3x+7}/{x-5}-{15+3x}/{x}-{25-3x}/{x^2-5x}=0</m>

<m>{3x^2+7x-(15+3x)(x-5)}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>{3x^2+7x-15x+75-3x^2+15x}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>{7x+75}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>7x+75=25-3x</m>

<m>10x=-50</m>

<m>x=-5</m>

<m>{6-z}/{1+z}-{2(4z-3)}/{z^2-1}=z/{1-z}</m>

<m>z<>pm 1</m>

<m>{6-z}/{1+z}-{8z-6}/{z^2-1}=z/{1-z}</m>

<m>{6-z}/{1+z}-z/{1-z}={8z-6}/{z^2-1}</m>

<m>{(6-z)(1-z)-z(1+z)}/{1-z^2}={8z-6}/{z^2-1}</m>

<m>{6-6z-z+z^2-z-z^2}/{1-z^2}={8z-6}/{z^2-1}</m>

<m>{-8z+6}/{1-z^2}={-8z+6}/{1-z^2}</m>

<m>z in bbR-delim{lbrace}{pm 1}{rbrace}</m>