Solve 1000=left(1+F/2^11right)2^25-16

$$1000 = \left( 1+ \frac{ F }{ { 2 }^{ 11 } } \right) { 2 }^{ 25-16 }$$

Solve for F

$$F=1952$$

Steps for Solving Linear Equation

Calculate 2 to the power of 11 and get 2048.

$$1000=\left(1+\frac{F}{2048}\right)\times 2^{25-16}$$

Subtract 16 from 25 to get 9.

$$1000=\left(1+\frac{F}{2048}\right)\times 2^{9}$$

Calculate 2 to the power of 9 and get 512.

$$1000=\left(1+\frac{F}{2048}\right)\times 512$$

Use the distributive property to multiply 1+\frac{F}{2048} by 512.

$$1000=512+512\times \frac{F}{2048}$$

Cancel out 2048, the greatest common factor in 512 and 2048.

$$1000=512+\frac{F}{4}$$

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

$$512+\frac{F}{4}=1000$$

Subtract 512 from both sides.

$$\frac{F}{4}=1000-512$$

Subtract 512 from 1000 to get 488.

$$\frac{F}{4}=488$$

Multiply both sides by 4.

$$F=488\times 4$$

Multiply 488 and 4 to get 1952.

$$F=1952$$