Solve 61/4+55/6x=12/3x

$$6 \frac { 1 } { 4 } + 5 \frac { 5 } { 6 } x= 1 \frac { 2 } { 3 } x$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

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

$$3\left(6\times 4+1\right)+2\left(5\times 6+5\right)x=4\left(1\times 3+2\right)x$$

Multiply 6 and 4 to get 24.

$$3\left(24+1\right)+2\left(5\times 6+5\right)x=4\left(1\times 3+2\right)x$$

Add 24 and 1 to get 25.

$$3\times 25+2\left(5\times 6+5\right)x=4\left(1\times 3+2\right)x$$

Multiply 3 and 25 to get 75.

$$75+2\left(5\times 6+5\right)x=4\left(1\times 3+2\right)x$$

Multiply 5 and 6 to get 30.

$$75+2\left(30+5\right)x=4\left(1\times 3+2\right)x$$

Add 30 and 5 to get 35.

$$75+2\times 35x=4\left(1\times 3+2\right)x$$

Multiply 2 and 35 to get 70.

$$75+70x=4\left(1\times 3+2\right)x$$

Multiply 1 and 3 to get 3.

$$75+70x=4\left(3+2\right)x$$

Add 3 and 2 to get 5.

$$75+70x=4\times 5x$$

Multiply 4 and 5 to get 20.

$$75+70x=20x$$

Subtract 20x from both sides.

$$75+70x-20x=0$$

Combine 70x and -20x to get 50x.

$$75+50x=0$$

Subtract 75 from both sides. Anything subtracted from zero gives its negation.

$$50x=-75$$

Divide both sides by 50.

$$x=\frac{-75}{50}$$

Reduce the fraction \frac{-75}{50} to lowest terms by extracting and canceling out 25.

$$x=-\frac{3}{2}$$