Solve 5/2x+6=3/4x+8

$$\frac { 5 } { 2 x + 6 } = \frac { 3 } { 4 x + 8 }$$

Solve for x

$$x = -\frac{11}{7} = -1\frac{4}{7} \approx -1.571428571$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,-2 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+2\right)\left(x+3\right), the least common multiple of 2x+6,4x+8.

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

Use the distributive property to multiply 2x+4 by 5.

$$10x+20=\left(x+3\right)\times 3$$

Use the distributive property to multiply x+3 by 3.

$$10x+20=3x+9$$

Subtract 3x from both sides.

$$10x+20-3x=9$$

Combine 10x and -3x to get 7x.

$$7x+20=9$$

Subtract 20 from both sides.

$$7x=9-20$$

Subtract 20 from 9 to get -11.

$$7x=-11$$

Divide both sides by 7.

$$x=\frac{-11}{7}$$

Fraction \frac{-11}{7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$x=-\frac{11}{7}$$