Solve x+4/3x=7+x/3x+7

$$\frac { x + 4 } { 3 x } = \frac { 7 + x } { 3 x + 7 }$$

Solve for x

$$x=14$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{7}{3},0 since division by zero is not defined. Multiply both sides of the equation by 3x\left(3x+7\right), the least common multiple of 3x,3x+7.

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

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

$$3x^{2}+19x+28=3x\left(7+x\right)$$

Use the distributive property to multiply 3x by 7+x.

$$3x^{2}+19x+28=21x+3x^{2}$$

Subtract 21x from both sides.

$$3x^{2}+19x+28-21x=3x^{2}$$

Combine 19x and -21x to get -2x.

$$3x^{2}-2x+28=3x^{2}$$

Subtract 3x^{2} from both sides.

$$3x^{2}-2x+28-3x^{2}=0$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-2x+28=0$$

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-28$$

Divide both sides by -2.

$$x=\frac{-28}{-2}$$

Divide -28 by -2 to get 14.

$$x=14$$