Solve 5/2x-3-3x-8/4x-6=7/9-6x-1/10x-15

$$\frac { 5 } { 2 x - 3 } - \frac { 3 x - 8 } { 4 x - 6 } = \frac { 7 } { 9 } - \frac { 6 x - 1 } { 10 x - 15 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 90\left(2x-3\right), the least common multiple of 2x-3,4x-6,9,10x-15.

$$90\times 5-45\left(3x-8\right)=90\left(2x-3\right)\times \frac{7}{9}-18\left(6x-1\right)$$

Multiply 90 and 5 to get 450.

$$450-45\left(3x-8\right)=90\left(2x-3\right)\times \frac{7}{9}-18\left(6x-1\right)$$

Use the distributive property to multiply -45 by 3x-8.

$$450-135x+360=90\left(2x-3\right)\times \frac{7}{9}-18\left(6x-1\right)$$

Add 450 and 360 to get 810.

$$810-135x=90\left(2x-3\right)\times \frac{7}{9}-18\left(6x-1\right)$$

Multiply 90 and \frac{7}{9} to get 70.

$$810-135x=70\left(2x-3\right)-18\left(6x-1\right)$$

Use the distributive property to multiply 70 by 2x-3.

$$810-135x=140x-210-18\left(6x-1\right)$$

Use the distributive property to multiply -18 by 6x-1.

$$810-135x=140x-210-108x+18$$

Combine 140x and -108x to get 32x.

$$810-135x=32x-210+18$$

Add -210 and 18 to get -192.

$$810-135x=32x-192$$

Subtract 32x from both sides.

$$810-135x-32x=-192$$

Combine -135x and -32x to get -167x.

$$810-167x=-192$$

Subtract 810 from both sides.

$$-167x=-192-810$$

Subtract 810 from -192 to get -1002.

$$-167x=-1002$$

Divide both sides by -167.

$$x=\frac{-1002}{-167}$$

Divide -1002 by -167 to get 6.

$$x=6$$