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

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

Solve for x

$$x=5000$$

Steps for Solving Linear Equation

Multiply 0 and 0 to get 0.

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

Multiply 0 and 6 to get 0.

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

Add 1 and 0 to get 1.

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

Calculate 1 to the power of -1 and get 1.

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

Multiply 1000 and 1 to get 1000.

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

Multiply 0 and 0 to get 0.

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

Multiply 0 and 6 to get 0.

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

Add 1 and 0 to get 1.

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

Calculate 1 to the power of -3 and get 1.

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

Multiply 4000 and 1 to get 4000.

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

Add 1000 and 4000 to get 5000.

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

Multiply 0 and 0 to get 0.

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

Multiply 0 and 6 to get 0.

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

Add 1 and 0 to get 1.

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

Calculate 1 to the power of -7 and get 1.

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

Multiply 10000 and 1 to get 10000.

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

Subtract 10000 from 5000 to get -5000.

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

Multiply 0 and 0 to get 0.

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

Multiply 0 and 6 to get 0.

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

Add 1 and 0 to get 1.

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

Calculate 1 to the power of -8 and get 1.

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

Add 5000 to both sides. Anything plus zero gives itself.

$$x\times 1=5000$$

Reorder the terms.

$$x=5000$$