Solve 4.5(x+6/6x)=1

$$4.5 ( \frac { x + 6 } { 6 x } ) = 1$$

Solve for x

$$x=18$$

Steps for Solving Linear Equation

Divide both sides by 4.5.

$$\frac{x+6}{6x}=\frac{1}{4.5}$$

Expand \frac{1}{4.5} by multiplying both numerator and the denominator by 10.

$$\frac{x+6}{6x}=\frac{10}{45}$$

Reduce the fraction \frac{10}{45} to lowest terms by extracting and canceling out 5.

$$\frac{x+6}{6x}=\frac{2}{9}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 18x, the least common multiple of 6x,9.

$$3\left(x+6\right)=4x$$

Use the distributive property to multiply 3 by x+6.

$$3x+18=4x$$

Subtract 4x from both sides.

$$3x+18-4x=0$$

Combine 3x and -4x to get -x.

$$-x+18=0$$

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$-x=-18$$

Multiply both sides by -1.

$$x=18$$