Solve 1/2+1/x=2cos9

$$\frac { 1 } { 2 } + \frac { 1 } { x } = 2 \cos 9$$

Solve for x

$$x=\frac{2500000000000000}{3688441702975689}\approx 0.677793009$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{1}{2} + \frac{1}{x} = 2 \cdot 0.9876883405951378$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,x.

$$2x\times \frac{1}{2}+2=2\times 0.9876883405951378\times 2x$$

Cancel out 2 and 2.

$$x+2=2\times 0.9876883405951378\times 2x$$

Multiply 2 and 0.9876883405951378 to get 1.9753766811902756.

$$x+2=1.9753766811902756\times 2x$$

Multiply 1.9753766811902756 and 2 to get 3.9507533623805512.

$$x+2=3.9507533623805512x$$

Subtract 3.9507533623805512x from both sides.

$$x+2-3.9507533623805512x=0$$

Combine x and -3.9507533623805512x to get -2.9507533623805512x.

$$-2.9507533623805512x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-2.9507533623805512x=-2$$

Divide both sides by -2.9507533623805512.

$$x=\frac{-2}{-2.9507533623805512}$$

Expand \frac{-2}{-2.9507533623805512} by multiplying both numerator and the denominator by 10000000000000000.

$$x=\frac{-20000000000000000}{-29507533623805512}$$

Reduce the fraction \frac{-20000000000000000}{-29507533623805512} to lowest terms by extracting and canceling out -8.

$$x=\frac{2500000000000000}{3688441702975689}$$