Whakaoti i te x/3*3+x/4*4+x/6-x5+(x/4-8)*2=504

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } - x 5 + ( \frac { x } { 4 } - 8 ) \cdot 2 = 504$$

Whakaoti mō x

$$x=\frac{3\left(x_{5}+520\right)}{8}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4,6.

$$4x\times 3+3x\times 4+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 4 ki te 3, ka 12.

$$12x+3x\times 4+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 3 ki te 4, ka 12.

$$12x+12x+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Pahekotia te 12x me 12x, ka 24x.

$$24x+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Pahekotia te 24x me 2x, ka 26x.

$$26x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 12 ki te 2, ka 24.

$$26x-12x_{5}+24\left(\frac{x}{4}-8\right)=6048$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24 ki te \frac{x}{4}-8.

$$26x-12x_{5}+24\times \frac{x}{4}-192=6048$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 24 me te 4.

$$26x-12x_{5}+6x-192=6048$$

Pahekotia te 26x me 6x, ka 32x.

$$32x-12x_{5}-192=6048$$

Me tāpiri te 12x_{5} ki ngā taha e rua.

$$32x-192=6048+12x_{5}$$

Me tāpiri te 192 ki ngā taha e rua.

$$32x=6048+12x_{5}+192$$

Tāpirihia te 6048 ki te 192, ka 6240.

$$32x=6240+12x_{5}$$

He hanga arowhānui tō te whārite.

$$32x=12x_{5}+6240$$

Whakawehea ngā taha e rua ki te 32.

$$\frac{32x}{32}=\frac{12x_{5}+6240}{32}$$

Mā te whakawehe ki te 32 ka wetekia te whakareanga ki te 32.

$$x=\frac{12x_{5}+6240}{32}$$

Whakawehe 6240+12x_{5} ki te 32.

$$x=\frac{3x_{5}}{8}+195$$

Whakaoti mō x_5

$$x_{5}=\frac{8\left(x-195\right)}{3}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4,6.

$$4x\times 3+3x\times 4+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 4 ki te 3, ka 12.

$$12x+3x\times 4+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 3 ki te 4, ka 12.

$$12x+12x+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Pahekotia te 12x me 12x, ka 24x.

$$24x+2x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Pahekotia te 24x me 2x, ka 26x.

$$26x-12x_{5}+12\left(\frac{x}{4}-8\right)\times 2=6048$$

Whakareatia te 12 ki te 2, ka 24.

$$26x-12x_{5}+24\left(\frac{x}{4}-8\right)=6048$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24 ki te \frac{x}{4}-8.

$$26x-12x_{5}+24\times \frac{x}{4}-192=6048$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 24 me te 4.

$$26x-12x_{5}+6x-192=6048$$

Pahekotia te 26x me 6x, ka 32x.

$$32x-12x_{5}-192=6048$$

Tangohia te 32x mai i ngā taha e rua.

$$-12x_{5}-192=6048-32x$$

Me tāpiri te 192 ki ngā taha e rua.

$$-12x_{5}=6048-32x+192$$

Tāpirihia te 6048 ki te 192, ka 6240.

$$-12x_{5}=6240-32x$$

Whakawehea ngā taha e rua ki te -12.

$$\frac{-12x_{5}}{-12}=\frac{6240-32x}{-12}$$

Mā te whakawehe ki te -12 ka wetekia te whakareanga ki te -12.

$$x_{5}=\frac{6240-32x}{-12}$$

Whakawehe 6240-32x ki te -12.

$$x_{5}=\frac{8x}{3}-520$$