Solve 1000=left(1+x/2^11right)2^26-16

$$1000 = \left( 1+ \frac{ x }{ { 2 }^{ 11 } } \right) { 2 }^{ 26-16 }$$

Solve for x

$$x=-48$$

Steps for Solving Linear Equation

Calculate 2 to the power of 11 and get 2048.

$$1000=\left(1+\frac{x}{2048}\right)\times 2^{26-16}$$

Subtract 16 from 26 to get 10.

$$1000=\left(1+\frac{x}{2048}\right)\times 2^{10}$$

Calculate 2 to the power of 10 and get 1024.

$$1000=\left(1+\frac{x}{2048}\right)\times 1024$$

Use the distributive property to multiply 1+\frac{x}{2048} by 1024.

$$1000=1024+1024\times \frac{x}{2048}$$

Cancel out 2048, the greatest common factor in 1024 and 2048.

$$1000=1024+\frac{x}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1024+\frac{x}{2}=1000$$

Subtract 1024 from both sides.

$$\frac{x}{2}=1000-1024$$

Subtract 1024 from 1000 to get -24.

$$\frac{x}{2}=-24$$

Multiply both sides by 2.

$$x=-24\times 2$$

Multiply -24 and 2 to get -48.

$$x=-48$$