Whakaoti i te 1000*left(1+006right)^-1+4000*left(1+006right)^-3-10000*left(1+006right)^-7+xleft(1+006right)^-8=0

$$1000 \times { \left(1+006 \right) }^{ -1 } +4000 \times { \left(1+006 \right) }^{ -3 } -10000 \times { \left(1+006 \right) }^{ -7 } +x { \left(1+006 \right) }^{ -8 } =0$$

Whakaoti mō x

$$x=5000$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 0 ki te 0, ka 0.

$$1000\left(1+0\times 6\right)^{-1}+4000\left(1+0\times 0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 6, ka 0.

$$1000\left(1+0\right)^{-1}+4000\left(1+0\times 0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tāpirihia te 1 ki te 0, ka 1.

$$1000\times 1^{-1}+4000\left(1+0\times 0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tātaihia te 1 mā te pū o -1, kia riro ko 1.

$$1000\times 1+4000\left(1+0\times 0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 1000 ki te 1, ka 1000.

$$1000+4000\left(1+0\times 0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 0, ka 0.

$$1000+4000\left(1+0\times 6\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 6, ka 0.

$$1000+4000\left(1+0\right)^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tāpirihia te 1 ki te 0, ka 1.

$$1000+4000\times 1^{-3}-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tātaihia te 1 mā te pū o -3, kia riro ko 1.

$$1000+4000\times 1-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 4000 ki te 1, ka 4000.

$$1000+4000-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tāpirihia te 1000 ki te 4000, ka 5000.

$$5000-10000\left(1+0\times 0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 0, ka 0.

$$5000-10000\left(1+0\times 6\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 6, ka 0.

$$5000-10000\left(1+0\right)^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tāpirihia te 1 ki te 0, ka 1.

$$5000-10000\times 1^{-7}+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tātaihia te 1 mā te pū o -7, kia riro ko 1.

$$5000-10000\times 1+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 10000 ki te 1, ka 10000.

$$5000-10000+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Tangohia te 10000 i te 5000, ka -5000.

$$-5000+x\left(1+0\times 0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 0, ka 0.

$$-5000+x\left(1+0\times 6\right)^{-8}=0$$

Whakareatia te 0 ki te 6, ka 0.

$$-5000+x\left(1+0\right)^{-8}=0$$

Tāpirihia te 1 ki te 0, ka 1.

$$-5000+x\times 1^{-8}=0$$

Tātaihia te 1 mā te pū o -8, kia riro ko 1.

$$-5000+x\times 1=0$$

Me tāpiri te 5000 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x\times 1=5000$$

Whakaraupapatia anō ngā kīanga tau.

$$x=5000$$