Solve 5x+2/10x-3=x-8/2x+3

$$\frac { 5 x + 2 } { 10 x - 3 } = \frac { x - 8 } { 2 x + 3 }$$

Solve for x

$$x=\frac{3}{17}\approx 0.176470588$$

Steps for Solving Linear Equation

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

$$\left(2x+3\right)\left(5x+2\right)=\left(10x-3\right)\left(x-8\right)$$

Use the distributive property to multiply 2x+3 by 5x+2 and combine like terms.

$$10x^{2}+19x+6=\left(10x-3\right)\left(x-8\right)$$

Use the distributive property to multiply 10x-3 by x-8 and combine like terms.

$$10x^{2}+19x+6=10x^{2}-83x+24$$

Subtract 10x^{2} from both sides.

$$10x^{2}+19x+6-10x^{2}=-83x+24$$

Combine 10x^{2} and -10x^{2} to get 0.

$$19x+6=-83x+24$$

Add 83x to both sides.

$$19x+6+83x=24$$

Combine 19x and 83x to get 102x.

$$102x+6=24$$

Subtract 6 from both sides.

$$102x=24-6$$

Subtract 6 from 24 to get 18.

$$102x=18$$

Divide both sides by 102.

$$x=\frac{18}{102}$$

Reduce the fraction \frac{18}{102} to lowest terms by extracting and canceling out 6.

$$x=\frac{3}{17}$$