Solve x/3+9/4=-5x/6+45/6

$$\frac { x } { 3 } + \frac { 9 } { 4 } = - \frac { 5 x } { 6 } + \frac { 45 } { 6 }$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$4x+27=-2\times 5x+2\times 45$$

Multiply -2 and 5 to get -10. Multiply 2 and 45 to get 90.

$$4x+27=-10x+90$$

Add 10x to both sides.

$$4x+27+10x=90$$

Combine 4x and 10x to get 14x.

$$14x+27=90$$

Subtract 27 from both sides.

$$14x=90-27$$

Subtract 27 from 90 to get 63.

$$14x=63$$

Divide both sides by 14.

$$x=\frac{63}{14}$$

Reduce the fraction \frac{63}{14} to lowest terms by extracting and canceling out 7.

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