Solve 6x-1/3x+2=4x-7/2x-5

$$\frac { 6 x - 1 } { 3 x + 2 } = \frac { 4 x - 7 } { 2 x - 5 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{3},\frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-5\right)\left(3x+2\right), the least common multiple of 3x+2,2x-5.

$$\left(2x-5\right)\left(6x-1\right)=\left(3x+2\right)\left(4x-7\right)$$

Use the distributive property to multiply 2x-5 by 6x-1 and combine like terms.

$$12x^{2}-32x+5=\left(3x+2\right)\left(4x-7\right)$$

Use the distributive property to multiply 3x+2 by 4x-7 and combine like terms.

$$12x^{2}-32x+5=12x^{2}-13x-14$$

Subtract 12x^{2} from both sides.

$$12x^{2}-32x+5-12x^{2}=-13x-14$$

Combine 12x^{2} and -12x^{2} to get 0.

$$-32x+5=-13x-14$$

Add 13x to both sides.

$$-32x+5+13x=-14$$

Combine -32x and 13x to get -19x.

$$-19x+5=-14$$

Subtract 5 from both sides.

$$-19x=-14-5$$

Subtract 5 from -14 to get -19.

$$-19x=-19$$

Divide both sides by -19.

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

Divide -19 by -19 to get 1.

$$x=1$$