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

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

Solve for x

$$x = -\frac{11}{9} = -1\frac{2}{9} \approx -1.222222222$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 2x+3 by 6x+7 and combine like terms.

$$12x^{2}+32x+21=\left(3x+2\right)\left(4x+5\right)$$

Use the distributive property to multiply 3x+2 by 4x+5 and combine like terms.

$$12x^{2}+32x+21=12x^{2}+23x+10$$

Subtract 12x^{2} from both sides.

$$12x^{2}+32x+21-12x^{2}=23x+10$$

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

$$32x+21=23x+10$$

Subtract 23x from both sides.

$$32x+21-23x=10$$

Combine 32x and -23x to get 9x.

$$9x+21=10$$

Subtract 21 from both sides.

$$9x=10-21$$

Subtract 21 from 10 to get -11.

$$9x=-11$$

Divide both sides by 9.

$$x=\frac{-11}{9}$$

Fraction \frac{-11}{9} can be rewritten as -\frac{11}{9} by extracting the negative sign.

$$x=-\frac{11}{9}$$