Whakaoti i te 1/5x-[3/2x-x-1/10-1/100(10x-40)]=frac{x-1}{5}-frac{3-x}{2}

$$\frac { 1 } { 5 } x - [ \frac { 3 } { 2 } x - \frac { x - 1 } { 10 } - \frac { 1 } { 100 } ( 10 x - 40 ) ] = \frac { x - 1 } { 5 } - \frac { 3 - x } { 2 }$$

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 100, arā, te tauraro pātahi he tino iti rawa te kitea o 5,2,10,100.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{100}\left(10x-40\right)\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{100} ki te 10x-40.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{100}\times 10x-\frac{1}{100}\left(-40\right)\right)=20\left(x-1\right)-50\left(3-x\right)$$

Tuhia te -\frac{1}{100}\times 10 hei hautanga kotahi.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}+\frac{-10}{100}x-\frac{1}{100}\left(-40\right)\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakahekea te hautanga \frac{-10}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{10}x-\frac{1}{100}\left(-40\right)\right)=20\left(x-1\right)-50\left(3-x\right)$$

Tuhia te -\frac{1}{100}\left(-40\right) hei hautanga kotahi.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{10}x+\frac{-\left(-40\right)}{100}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakareatia te -1 ki te -40, ka 40.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{10}x+\frac{40}{100}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakahekea te hautanga \frac{40}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$20x-100\left(\frac{3}{2}x-\frac{x-1}{10}-\frac{1}{10}x+\frac{2}{5}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Pahekotia te \frac{3}{2}x me -\frac{1}{10}x, ka \frac{7}{5}x.

$$20x-100\left(\frac{7}{5}x-\frac{x-1}{10}+\frac{2}{5}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 10 me 5 ko 10. Whakareatia \frac{2}{5} ki te \frac{2}{2}.

$$20x-100\left(\frac{7}{5}x-\frac{x-1}{10}+\frac{2\times 2}{10}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Tā te mea he rite te tauraro o -\frac{x-1}{10} me \frac{2\times 2}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$20x-100\left(\frac{7}{5}x+\frac{-\left(x-1\right)+2\times 2}{10}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Mahia ngā whakarea i roto o -\left(x-1\right)+2\times 2.

$$20x-100\left(\frac{7}{5}x+\frac{-x+1+4}{10}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakakotahitia ngā kupu rite i -x+1+4.

$$20x-100\left(\frac{7}{5}x+\frac{-x+5}{10}\right)=20\left(x-1\right)-50\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 20 ki te x-1.

$$20x-100\left(\frac{7}{5}x+\frac{-x+5}{10}\right)=20x-20-50\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -50 ki te 3-x.

$$20x-100\left(\frac{7}{5}x+\frac{-x+5}{10}\right)=20x-20-150+50x$$

Tangohia te 150 i te -20, ka -170.

$$20x-100\left(\frac{7}{5}x+\frac{-x+5}{10}\right)=20x-170+50x$$

Pahekotia te 20x me 50x, ka 70x.

$$20x-100\left(\frac{7}{5}x+\frac{-x+5}{10}\right)=70x-170$$

Whakawehea ia wā o -x+5 ki te 10, kia riro ko -\frac{1}{10}x+\frac{1}{2}.

$$20x-100\left(\frac{7}{5}x-\frac{1}{10}x+\frac{1}{2}\right)=70x-170$$

Pahekotia te \frac{7}{5}x me -\frac{1}{10}x, ka \frac{13}{10}x.

$$20x-100\left(\frac{13}{10}x+\frac{1}{2}\right)=70x-170$$

Whakamahia te āhuatanga tohatoha hei whakarea te -100 ki te \frac{13}{10}x+\frac{1}{2}.

$$20x-100\times \frac{13}{10}x-100\times \frac{1}{2}=70x-170$$

Tuhia te -100\times \frac{13}{10} hei hautanga kotahi.

$$20x+\frac{-100\times 13}{10}x-100\times \frac{1}{2}=70x-170$$

Whakareatia te -100 ki te 13, ka -1300.

$$20x+\frac{-1300}{10}x-100\times \frac{1}{2}=70x-170$$

Whakawehea te -1300 ki te 10, kia riro ko -130.

$$20x-130x-100\times \frac{1}{2}=70x-170$$

Whakareatia te -100 ki te \frac{1}{2}, ka \frac{-100}{2}.

$$20x-130x+\frac{-100}{2}=70x-170$$

Whakawehea te -100 ki te 2, kia riro ko -50.

$$20x-130x-50=70x-170$$

Pahekotia te 20x me -130x, ka -110x.

$$-110x-50=70x-170$$

Tangohia te 70x mai i ngā taha e rua.

$$-110x-50-70x=-170$$

Pahekotia te -110x me -70x, ka -180x.

$$-180x-50=-170$$

Me tāpiri te 50 ki ngā taha e rua.

$$-180x=-170+50$$

Tāpirihia te -170 ki te 50, ka -120.

$$-180x=-120$$

Whakawehea ngā taha e rua ki te -180.

$$x=\frac{-120}{-180}$$

Whakahekea te hautanga \frac{-120}{-180} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -60.

$$x=\frac{2}{3}$$