Solve 4x-1/5+x+2/2x-7=8x-3/10-13/10

$$\frac { 4 x - 1 } { 5 } + \frac { x + 2 } { 2 x - 7 } = \frac { 8 x - 3 } { 10 } - \frac { 13 } { 10 }$$

Solve for x

$$x = \frac{39}{19} = 2\frac{1}{19} \approx 2.052631579$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{7}{2} since division by zero is not defined. Multiply both sides of the equation by 10\left(2x-7\right), the least common multiple of 5,2x-7,10.

$$\left(4x-14\right)\left(4x-1\right)+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Use the distributive property to multiply 4x-14 by 4x-1 and combine like terms.

$$16x^{2}-60x+14+10\left(x+2\right)=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Use the distributive property to multiply 10 by x+2.

$$16x^{2}-60x+14+10x+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Combine -60x and 10x to get -50x.

$$16x^{2}-50x+14+20=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Add 14 and 20 to get 34.

$$16x^{2}-50x+34=\left(2x-7\right)\left(8x-3\right)+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Use the distributive property to multiply 2x-7 by 8x-3 and combine like terms.

$$16x^{2}-50x+34=16x^{2}-62x+21+10\left(2x-7\right)\left(-\frac{13}{10}\right)$$

Multiply 10 and -\frac{13}{10} to get -13.

$$16x^{2}-50x+34=16x^{2}-62x+21-13\left(2x-7\right)$$

Use the distributive property to multiply -13 by 2x-7.

$$16x^{2}-50x+34=16x^{2}-62x+21-26x+91$$

Combine -62x and -26x to get -88x.

$$16x^{2}-50x+34=16x^{2}-88x+21+91$$

Add 21 and 91 to get 112.

$$16x^{2}-50x+34=16x^{2}-88x+112$$

Subtract 16x^{2} from both sides.

$$16x^{2}-50x+34-16x^{2}=-88x+112$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-50x+34=-88x+112$$

Add 88x to both sides.

$$-50x+34+88x=112$$

Combine -50x and 88x to get 38x.

$$38x+34=112$$

Subtract 34 from both sides.

$$38x=112-34$$

Subtract 34 from 112 to get 78.

$$38x=78$$

Divide both sides by 38.

$$x=\frac{78}{38}$$

Reduce the fraction \frac{78}{38} to lowest terms by extracting and canceling out 2.

$$x=\frac{39}{19}$$