Réitigh 0.4x+0.9/0.5-0.1x-0.5/0.2=0.03+0.02x/0.03

$$\frac { 0.4 x + 0.9 } { 0.5 } - \frac { 0.1 x - 0.5 } { 0.2 } = \frac { 0.03 + 0.02 x } { 0.03 }$$

Réitigh do x.

$$x=9$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Roinn 0.4x+0.9 faoi 0.5 chun \frac{0.4x}{0.5}+\frac{0.9}{0.5} a fháil.

$$\frac{0.4x}{0.5}+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Roinn 0.4x faoi 0.5 chun 0.8x a fháil.

$$0.8x+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Fairsingigh \frac{0.9}{0.5} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

$$0.8x+\frac{9}{5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Roinn 0.1x-0.5 faoi 0.2 chun \frac{0.1x}{0.2}+\frac{-0.5}{0.2} a fháil.

$$0.8x+\frac{9}{5}-\left(\frac{0.1x}{0.2}+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Roinn 0.1x faoi 0.2 chun 0.5x a fháil.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Fairsingigh \frac{-0.5}{0.2} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Is féidir an codán \frac{-5}{2} a athscríobh mar -\frac{5}{2} ach an comhartha diúltach a bhaint.

$$0.8x+\frac{9}{5}-\left(0.5x-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Chun an mhalairt ar 0.5x-\frac{5}{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$0.8x+\frac{9}{5}-0.5x-\left(-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Tá \frac{5}{2} urchomhairleach le -\frac{5}{2}.

$$0.8x+\frac{9}{5}-0.5x+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Comhcheangail 0.8x agus -0.5x chun 0.3x a fháil.

$$0.3x+\frac{9}{5}+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Is é an t-iolrach is lú coitianta de 5 agus 2 ná 10. Coinbhéartaigh \frac{9}{5} agus \frac{5}{2} chuig codáin a bhfuil an t-ainmneoir 10 acu.

$$0.3x+\frac{18}{10}+\frac{25}{10}=\frac{0.03+0.02x}{0.03}$$

Tá an t-ainmneoir céanna ag \frac{18}{10} agus \frac{25}{10} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$0.3x+\frac{18+25}{10}=\frac{0.03+0.02x}{0.03}$$

Suimigh 18 agus 25 chun 43 a fháil.

$$0.3x+\frac{43}{10}=\frac{0.03+0.02x}{0.03}$$

Roinn 0.03+0.02x faoi 0.03 chun \frac{0.03}{0.03}+\frac{0.02x}{0.03} a fháil.

$$0.3x+\frac{43}{10}=\frac{0.03}{0.03}+\frac{0.02x}{0.03}$$

Roinn 0.03 faoi 0.03 chun 1 a fháil.

$$0.3x+\frac{43}{10}=1+\frac{0.02x}{0.03}$$

Roinn 0.02x faoi 0.03 chun \frac{2}{3}x a fháil.

$$0.3x+\frac{43}{10}=1+\frac{2}{3}x$$

Bain \frac{2}{3}x ón dá thaobh.

$$0.3x+\frac{43}{10}-\frac{2}{3}x=1$$

Comhcheangail 0.3x agus -\frac{2}{3}x chun -\frac{11}{30}x a fháil.

$$-\frac{11}{30}x+\frac{43}{10}=1$$

Bain \frac{43}{10} ón dá thaobh.

$$-\frac{11}{30}x=1-\frac{43}{10}$$

Coinbhéartaigh 1 i gcodán \frac{10}{10}.

$$-\frac{11}{30}x=\frac{10}{10}-\frac{43}{10}$$

Tá an t-ainmneoir céanna ag \frac{10}{10} agus \frac{43}{10} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$-\frac{11}{30}x=\frac{10-43}{10}$$

Dealaigh 43 ó 10 chun -33 a fháil.

$$-\frac{11}{30}x=-\frac{33}{10}$$

Roinn an dá thaobh faoi -\frac{11}{30}.

$$x=\frac{-\frac{33}{10}}{-\frac{11}{30}}$$

Scríobh \frac{-\frac{33}{10}}{-\frac{11}{30}} mar chodán aonair.

$$x=\frac{-33}{10\left(-\frac{11}{30}\right)}$$

Méadaigh 10 agus -\frac{11}{30} chun -\frac{11}{3} a fháil.

$$x=\frac{-33}{-\frac{11}{3}}$$