Solve 6x-1/18-3left(x+2right)/5x-6=1+3x/9

$$\frac{ 6x-1 }{ 18 } - \frac{ 3 \left( x+2 \right) }{ 5x-6 } = \frac{ 1+3x }{ 9 }$$

Solve for x

$$x = -\frac{30}{23} = -1\frac{7}{23} \approx -1.304347826$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{6}{5} since division by zero is not defined. Multiply both sides of the equation by 18\left(5x-6\right), the least common multiple of 18,5x-6,9.

$$\left(5x-6\right)\left(6x-1\right)-18\times 3\left(x+2\right)=\left(10x-12\right)\left(1+3x\right)$$

Use the distributive property to multiply 5x-6 by 6x-1 and combine like terms.

$$30x^{2}-41x+6-18\times 3\left(x+2\right)=\left(10x-12\right)\left(1+3x\right)$$

Multiply -18 and 3 to get -54.

$$30x^{2}-41x+6-54\left(x+2\right)=\left(10x-12\right)\left(1+3x\right)$$

Use the distributive property to multiply -54 by x+2.

$$30x^{2}-41x+6-54x-108=\left(10x-12\right)\left(1+3x\right)$$

Combine -41x and -54x to get -95x.

$$30x^{2}-95x+6-108=\left(10x-12\right)\left(1+3x\right)$$

Subtract 108 from 6 to get -102.

$$30x^{2}-95x-102=\left(10x-12\right)\left(1+3x\right)$$

Use the distributive property to multiply 10x-12 by 1+3x and combine like terms.

$$30x^{2}-95x-102=-26x+30x^{2}-12$$

Add 26x to both sides.

$$30x^{2}-95x-102+26x=30x^{2}-12$$

Combine -95x and 26x to get -69x.

$$30x^{2}-69x-102=30x^{2}-12$$

Subtract 30x^{2} from both sides.

$$30x^{2}-69x-102-30x^{2}=-12$$

Combine 30x^{2} and -30x^{2} to get 0.

$$-69x-102=-12$$

Add 102 to both sides.

$$-69x=-12+102$$

Add -12 and 102 to get 90.

$$-69x=90$$

Divide both sides by -69.

$$x=\frac{90}{-69}$$

Reduce the fraction \frac{90}{-69} to lowest terms by extracting and canceling out 3.

$$x=-\frac{30}{23}$$