Solve 1/x+2(x-3)/4=1.5x-2/3

$$\frac { 1 } { x } + \frac { 2 ( x - 3 ) } { 4 } = \frac { 1.5 x - 2 } { 3 }$$

Solve for x

$$x=1.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x, the least common multiple of x,4,3.

$$12+3x\times 2\left(x-3\right)=4x\left(1.5x-2\right)$$

Multiply 3 and 2 to get 6.

$$12+6x\left(x-3\right)=4x\left(1.5x-2\right)$$

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

$$12+6x^{2}-18x=4x\left(1.5x-2\right)$$

Use the distributive property to multiply 4x by 1.5x-2.

$$12+6x^{2}-18x=6x^{2}-8x$$

Subtract 6x^{2} from both sides.

$$12+6x^{2}-18x-6x^{2}=-8x$$

Combine 6x^{2} and -6x^{2} to get 0.

$$12-18x=-8x$$

Add 8x to both sides.

$$12-18x+8x=0$$

Combine -18x and 8x to get -10x.

$$12-10x=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-12$$

Divide both sides by -10.

$$x=\frac{-12}{-10}$$

Reduce the fraction \frac{-12}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{6}{5}$$