Solve 5(x-2)+6/3x=5x/11-3(2-x)

$$\frac { 5 ( x - 2 ) + 6 } { 3 x } = \frac { 5 x } { 11 - 3 ( 2 - x ) }$$

Solve for x

$$x = \frac{20}{13} = 1\frac{7}{13} \approx 1.538461538$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{3},0 since division by zero is not defined. Multiply both sides of the equation by 3x\left(3x+5\right), the least common multiple of 3x,11-3\left(2-x\right).

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

Use the distributive property to multiply 5 by x-2.

$$\left(3x+5\right)\left(5x-10+6\right)=3x\times 5x$$

Add -10 and 6 to get -4.

$$\left(3x+5\right)\left(5x-4\right)=3x\times 5x$$

Use the distributive property to multiply 3x+5 by 5x-4 and combine like terms.

$$15x^{2}+13x-20=3x\times 5x$$

Multiply x and x to get x^{2}.

$$15x^{2}+13x-20=3x^{2}\times 5$$

Multiply 3 and 5 to get 15.

$$15x^{2}+13x-20=15x^{2}$$

Subtract 15x^{2} from both sides.

$$15x^{2}+13x-20-15x^{2}=0$$

Combine 15x^{2} and -15x^{2} to get 0.

$$13x-20=0$$

Add 20 to both sides. Anything plus zero gives itself.

$$13x=20$$

Divide both sides by 13.

$$x=\frac{20}{13}$$