Solve 1000=left(1+F/2^11right)2^24-16

$$1000 = \left( 1+ \frac{ F }{ { 2 }^{ 11 } } \right) { 2 }^{ 24-16 }$$

Solve for F

$$F=5952$$

Steps for Solving Linear Equation

Calculate 2 to the power of 11 and get 2048.

$$1000=\left(1+\frac{F}{2048}\right)\times 2^{24-16}$$

Subtract 16 from 24 to get 8.

$$1000=\left(1+\frac{F}{2048}\right)\times 2^{8}$$

Calculate 2 to the power of 8 and get 256.

$$1000=\left(1+\frac{F}{2048}\right)\times 256$$

Use the distributive property to multiply 1+\frac{F}{2048} by 256.

$$1000=256+256\times \frac{F}{2048}$$

Cancel out 2048, the greatest common factor in 256 and 2048.

$$1000=256+\frac{F}{8}$$

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

$$256+\frac{F}{8}=1000$$

Subtract 256 from both sides.

$$\frac{F}{8}=1000-256$$

Subtract 256 from 1000 to get 744.

$$\frac{F}{8}=744$$

Multiply both sides by 8.

$$F=744\times 8$$

Multiply 744 and 8 to get 5952.

$$F=5952$$