Whakaoti i te 0.2yquad(4)^2(2x-1)/0.01-2.5=0.2-20x/0.2-3.5

$$0.2 y \quad ( 4 ) ^ { 2 } \frac { ( 2 x - 1 ) } { 0.01 } - 2.5 = \frac { 0.2 - 20 x } { 0.2 } - 3.5$$

Whakaoti mō x

$$x=\frac{16y}{32y+5}$$

$$y\neq -\frac{5}{32}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$0.2y\times 16\times \frac{2x-1}{0.01}-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakareatia te 0.2 ki te 16, ka 3.2.

$$3.2y\times \frac{2x-1}{0.01}-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea ia wā o 2x-1 ki te 0.01, kia riro ko \frac{2x}{0.01}+\frac{-1}{0.01}.

$$3.2y\left(\frac{2x}{0.01}+\frac{-1}{0.01}\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea te 2x ki te 0.01, kia riro ko 200x.

$$3.2y\left(200x+\frac{-1}{0.01}\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakarohaina te \frac{-1}{0.01} mā te whakarea i te taurunga me te tauraro ki te 100. Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$3.2y\left(200x-100\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3.2y ki te 200x-100.

$$640xy-320y-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea ia wā o 0.2-20x ki te 0.2, kia riro ko \frac{0.2}{0.2}+\frac{-20x}{0.2}.

$$640xy-320y-2.5=\frac{0.2}{0.2}+\frac{-20x}{0.2}-3.5$$

Whakawehea te 0.2 ki te 0.2, kia riro ko 1.

$$640xy-320y-2.5=1+\frac{-20x}{0.2}-3.5$$

Whakawehea te -20x ki te 0.2, kia riro ko -100x.

$$640xy-320y-2.5=1-100x-3.5$$

Tangohia te 3.5 i te 1, ka -2.5.

$$640xy-320y-2.5=-2.5-100x$$

Me tāpiri te 100x ki ngā taha e rua.

$$640xy-320y-2.5+100x=-2.5$$

Me tāpiri te 320y ki ngā taha e rua.

$$640xy-2.5+100x=-2.5+320y$$

Me tāpiri te 2.5 ki ngā taha e rua.

$$640xy+100x=-2.5+320y+2.5$$

Tāpirihia te -2.5 ki te 2.5, ka 0.

$$640xy+100x=320y$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(640y+100\right)x=320y$$

Whakawehea ngā taha e rua ki te 640y+100.

$$\frac{\left(640y+100\right)x}{640y+100}=\frac{320y}{640y+100}$$

Mā te whakawehe ki te 640y+100 ka wetekia te whakareanga ki te 640y+100.

$$x=\frac{320y}{640y+100}$$

Whakawehe 320y ki te 640y+100.

$$x=\frac{16y}{32y+5}$$

Whakaoti mō y

$$y=-\frac{5x}{16\left(2x-1\right)}$$

$$x\neq \frac{1}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$0.2y\times 16\times \frac{2x-1}{0.01}-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakareatia te 0.2 ki te 16, ka 3.2.

$$3.2y\times \frac{2x-1}{0.01}-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea ia wā o 2x-1 ki te 0.01, kia riro ko \frac{2x}{0.01}+\frac{-1}{0.01}.

$$3.2y\left(\frac{2x}{0.01}+\frac{-1}{0.01}\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea te 2x ki te 0.01, kia riro ko 200x.

$$3.2y\left(200x+\frac{-1}{0.01}\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakarohaina te \frac{-1}{0.01} mā te whakarea i te taurunga me te tauraro ki te 100. Ka whakawehea he tau ki te tahi, hua ai ko ia anō.

$$3.2y\left(200x-100\right)-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3.2y ki te 200x-100.

$$640xy-320y-2.5=\frac{0.2-20x}{0.2}-3.5$$

Whakawehea ia wā o 0.2-20x ki te 0.2, kia riro ko \frac{0.2}{0.2}+\frac{-20x}{0.2}.

$$640xy-320y-2.5=\frac{0.2}{0.2}+\frac{-20x}{0.2}-3.5$$

Whakawehea te 0.2 ki te 0.2, kia riro ko 1.

$$640xy-320y-2.5=1+\frac{-20x}{0.2}-3.5$$

Whakawehea te -20x ki te 0.2, kia riro ko -100x.

$$640xy-320y-2.5=1-100x-3.5$$

Tangohia te 3.5 i te 1, ka -2.5.

$$640xy-320y-2.5=-2.5-100x$$

Me tāpiri te 2.5 ki ngā taha e rua.

$$640xy-320y=-2.5-100x+2.5$$

Tāpirihia te -2.5 ki te 2.5, ka 0.

$$640xy-320y=-100x$$

Pahekotia ngā kīanga tau katoa e whai ana i te y.

$$\left(640x-320\right)y=-100x$$

Whakawehea ngā taha e rua ki te 640x-320.

$$\frac{\left(640x-320\right)y}{640x-320}=-\frac{100x}{640x-320}$$

Mā te whakawehe ki te 640x-320 ka wetekia te whakareanga ki te 640x-320.

$$y=-\frac{100x}{640x-320}$$

Whakawehe -100x ki te 640x-320.

$$y=-\frac{5x}{16\left(2x-1\right)}$$