Solve 3.66=1.2756*(1+10*10^3/x)

$$3.66 = 1.2756 \times ( 1 + \frac { 10 \times 10 ^ { 3 } } { x } )$$

Solve for x

$$x = \frac{10630000}{1987} = 5349\frac{1537}{1987} \approx 5349.773527932$$

Steps for Solving Linear Equation

Divide both sides by 1.2756.

$$\frac{3.66}{1.2756}=1+\frac{10\times 10^{3}}{x}$$

Expand \frac{3.66}{1.2756} by multiplying both numerator and the denominator by 10000.

$$\frac{36600}{12756}=1+\frac{10\times 10^{3}}{x}$$

Reduce the fraction \frac{36600}{12756} to lowest terms by extracting and canceling out 12.

$$\frac{3050}{1063}=1+\frac{10\times 10^{3}}{x}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1063x, the least common multiple of 1063,x.

$$3050x=1063x+1063\times 10\times 10^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3050x=1063x+1063\times 10^{4}$$

Calculate 10 to the power of 4 and get 10000.

$$3050x=1063x+1063\times 10000$$

Multiply 1063 and 10000 to get 10630000.

$$3050x=1063x+10630000$$

Subtract 1063x from both sides.

$$3050x-1063x=10630000$$

Combine 3050x and -1063x to get 1987x.

$$1987x=10630000$$

Divide both sides by 1987.

$$x=\frac{10630000}{1987}$$