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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{3},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-1\right)\left(3x+2\right), the least common multiple of 3x+2,3x-1.

$$\left(3x-1\right)\left(5x-10\right)=\left(3x+2\right)\left(5x-7\right)$$

Use the distributive property to multiply 3x-1 by 5x-10 and combine like terms.

$$15x^{2}-35x+10=\left(3x+2\right)\left(5x-7\right)$$

Use the distributive property to multiply 3x+2 by 5x-7 and combine like terms.

$$15x^{2}-35x+10=15x^{2}-11x-14$$

Subtract 15x^{2} from both sides.

$$15x^{2}-35x+10-15x^{2}=-11x-14$$

Combine 15x^{2} and -15x^{2} to get 0.

$$-35x+10=-11x-14$$

Add 11x to both sides.

$$-35x+10+11x=-14$$

Combine -35x and 11x to get -24x.

$$-24x+10=-14$$

Subtract 10 from both sides.

$$-24x=-14-10$$

Subtract 10 from -14 to get -24.

$$-24x=-24$$

Divide both sides by -24.

$$x=\frac{-24}{-24}$$

Divide -24 by -24 to get 1.

$$x=1$$