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

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

Solvi għal x

$$x=9$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Iddividi kull terminu ta' 0.4x+0.9 b'0.5 biex tikseb\frac{0.4x}{0.5}+\frac{0.9}{0.5}.

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

Iddividi 0.4x b'0.5 biex tikseb0.8x.

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

Espandi \frac{0.9}{0.5} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Iddividi kull terminu ta' 0.1x-0.5 b'0.2 biex tikseb\frac{0.1x}{0.2}+\frac{-0.5}{0.2}.

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

Iddividi 0.1x b'0.2 biex tikseb0.5x.

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

Espandi \frac{-0.5}{0.2} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Frazzjoni \frac{-5}{2} tista' tinkiteb mill-ġdid bħala -\frac{5}{2} bl-estrazzjoni tas-sinjal negattiv.

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

Biex issib l-oppost ta' 0.5x-\frac{5}{2}, sib l-oppost ta' kull terminu.

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

L-oppost ta' -\frac{5}{2} huwa \frac{5}{2}.

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

Ikkombina 0.8x u -0.5x biex tikseb 0.3x.

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

L-inqas multipli komuni ta' 5 u 2 huwa 10. Ikkonverti \frac{9}{5} u \frac{5}{2} fi frazzjonijiet bid-denominatur 10.

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

Billi \frac{18}{10} u \frac{25}{10} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Żid 18 u 25 biex tikseb 43.

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

Iddividi kull terminu ta' 0.03+0.02x b'0.03 biex tikseb\frac{0.03}{0.03}+\frac{0.02x}{0.03}.

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

Iddividi 0.03 b'0.03 biex tikseb1.

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

Iddividi 0.02x b'0.03 biex tikseb\frac{2}{3}x.

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

Naqqas \frac{2}{3}x miż-żewġ naħat.

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

Ikkombina 0.3x u -\frac{2}{3}x biex tikseb -\frac{11}{30}x.

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

Naqqas \frac{43}{10} miż-żewġ naħat.

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

Ikkonverti 1 fi frazzjoni \frac{10}{10}.

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

Billi \frac{10}{10} u \frac{43}{10} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

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

Naqqas 43 minn 10 biex tikseb -33.

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

Iddividi ż-żewġ naħat b'-\frac{11}{30}.

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

Esprimi \frac{-\frac{33}{10}}{-\frac{11}{30}} bħala frazzjoni waħda.

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

Immultiplika 10 u -\frac{11}{30} biex tikseb -\frac{11}{3}.

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