Solve 7x+2/14x-3=x-8/2x+3

$$\frac { 7 x + 2 } { 14 x - 3 } = \frac { x - 8 } { 2 x + 3 }$$

Solve for x

$$x=\frac{9}{70}\approx 0.128571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{3}{2},\frac{3}{14} since division by zero is not defined. Multiply both sides of the equation by \left(14x-3\right)\left(2x+3\right), the least common multiple of 14x-3,2x+3.

$$\left(2x+3\right)\left(7x+2\right)=\left(14x-3\right)\left(x-8\right)$$

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

$$14x^{2}+25x+6=\left(14x-3\right)\left(x-8\right)$$

Use the distributive property to multiply 14x-3 by x-8 and combine like terms.

$$14x^{2}+25x+6=14x^{2}-115x+24$$

Subtract 14x^{2} from both sides.

$$14x^{2}+25x+6-14x^{2}=-115x+24$$

Combine 14x^{2} and -14x^{2} to get 0.

$$25x+6=-115x+24$$

Add 115x to both sides.

$$25x+6+115x=24$$

Combine 25x and 115x to get 140x.

$$140x+6=24$$

Subtract 6 from both sides.

$$140x=24-6$$

Subtract 6 from 24 to get 18.

$$140x=18$$

Divide both sides by 140.

$$x=\frac{18}{140}$$

Reduce the fraction \frac{18}{140} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{70}$$