Solve sin72-3/x=sin312/2558

$$\frac { \sin 72 - 3 } { x } = \frac { \sin 312 } { 2558 }$$

Solve for x

$$x = \frac{26205987156584986735}{3715724127386973} = 7052\frac{2700610252055076}{3715724127386973} \approx 7052.726805909$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.9510565162951535 - 3}{x} = \frac{-0.7431448254773946}{2558}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2558x, the least common multiple of x,2558.

$$2558\left(0.9510565162951535-3\right)=x\left(-0.7431448254773946\right)$$

Subtract 3 from 0.9510565162951535 to get -2.0489434837048465.

$$2558\left(-2.0489434837048465\right)=x\left(-0.7431448254773946\right)$$

Multiply 2558 and -2.0489434837048465 to get -5241.197431316997347.

$$-5241.197431316997347=x\left(-0.7431448254773946\right)$$

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

$$x\left(-0.7431448254773946\right)=-5241.197431316997347$$

Divide both sides by -0.7431448254773946.

$$x=\frac{-5241.197431316997347}{-0.7431448254773946}$$

Expand \frac{-5241.197431316997347}{-0.7431448254773946} by multiplying both numerator and the denominator by 10000000000000000.

$$x=\frac{-52411974313169973470}{-7431448254773946}$$

Reduce the fraction \frac{-52411974313169973470}{-7431448254773946} to lowest terms by extracting and canceling out -2.

$$x=\frac{26205987156584986735}{3715724127386973}$$