Issolvi 9/2x+1-8x/2x-1=-4

$$\frac { 9 } { 2 x + 1 } - \frac { 8 x } { 2 x - 1 } = - 4$$

Solvi għal x

$$x = \frac{13}{10} = 1\frac{3}{10} = 1.3$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri -\frac{1}{2},\frac{1}{2} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(2x-1\right)\left(2x+1\right), l-inqas denominatur komuni ta' 2x+1,2x-1.

$$\left(2x-1\right)\times 9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x-1 b'9.

$$18x-9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x+1 b'8.

$$18x-9-\left(16x+8\right)x=-4\left(2x-1\right)\left(2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 16x+8 b'x.

$$18x-9-\left(16x^{2}+8x\right)=-4\left(2x-1\right)\left(2x+1\right)$$

Biex issib l-oppost ta' 16x^{2}+8x, sib l-oppost ta' kull terminu.

$$18x-9-16x^{2}-8x=-4\left(2x-1\right)\left(2x+1\right)$$

Ikkombina 18x u -8x biex tikseb 10x.

$$10x-9-16x^{2}=-4\left(2x-1\right)\left(2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika -4 b'2x-1.

$$10x-9-16x^{2}=\left(-8x+4\right)\left(2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika -8x+4 b'2x+1 u kkombina termini simili.

$$10x-9-16x^{2}=-16x^{2}+4$$

Żid 16x^{2} maż-żewġ naħat.

$$10x-9-16x^{2}+16x^{2}=4$$

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

$$10x-9=4$$

Żid 9 maż-żewġ naħat.

$$10x=4+9$$

Żid 4 u 9 biex tikseb 13.

$$10x=13$$

Iddividi ż-żewġ naħat b'10.

$$x=\frac{13}{10}$$