Issolvi 4x-1/5+x+2/2x-7=8x-3/10-13/10

$$\frac { 4 x - 1 } { 5 } + \frac { x + 2 } { 2 x - 7 } = \frac { 8 x - 3 } { 10 } - \frac { 13 } { 10 }$$

Solvi għal x

$$x = \frac{39}{19} = 2\frac{1}{19} \approx 2.052631579$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal \frac{7}{2} billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'10\left(2x-7\right), l-inqas denominatur komuni ta' 5,2x-7,10.

$$\left(4x-14\right)\left(4x-1\right)+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 4x-14 b'4x-1 u kkombina termini simili.

$$16x^{2}-60x+14+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 10 b'x+2.

$$16x^{2}-60x+14+10x+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Ikkombina -60x u 10x biex tikseb -50x.

$$16x^{2}-50x+14+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Żid 14 u 20 biex tikseb 34.

$$16x^{2}-50x+34=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x-7 b'8x-3 u kkombina termini simili.

$$16x^{2}-50x+34=16x^{2}-62x+21+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Immultiplika 10 u -\frac{13}{10} biex tikseb -13.

$$16x^{2}-50x+34=16x^{2}-62x+21-13\left(2x-7\right)$$

Uża l-propjetà distributtiva biex timmultiplika -13 b'2x-7.

$$16x^{2}-50x+34=16x^{2}-62x+21-26x+91$$

Ikkombina -62x u -26x biex tikseb -88x.

$$16x^{2}-50x+34=16x^{2}-88x+21+91$$

Żid 21 u 91 biex tikseb 112.

$$16x^{2}-50x+34=16x^{2}-88x+112$$

Naqqas 16x^{2} miż-żewġ naħat.

$$16x^{2}-50x+34-16x^{2}=-88x+112$$

Ikkombina 16x^{2} u -16x^{2} biex tikseb 0.

$$-50x+34=-88x+112$$

Żid 88x maż-żewġ naħat.

$$-50x+34+88x=112$$

Ikkombina -50x u 88x biex tikseb 38x.

$$38x+34=112$$

Naqqas 34 miż-żewġ naħat.

$$38x=112-34$$

Naqqas 34 minn 112 biex tikseb 78.

$$38x=78$$

Iddividi ż-żewġ naħat b'38.

$$x=\frac{78}{38}$$

Naqqas il-frazzjoni \frac{78}{38} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$x=\frac{39}{19}$$