Solve 4x-7/12x+3=x-16/3x+5

$$\frac{ 4x-7 }{ 12x+3 } = \frac{ x-16 }{ 3x+5 }$$

Solve for x

$$x=-\frac{13}{188}\approx -0.069148936$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{3},-\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by 3\left(3x+5\right)\left(4x+1\right), the least common multiple of 12x+3,3x+5.

$$\left(3x+5\right)\left(4x-7\right)=\left(12x+3\right)\left(x-16\right)$$

Use the distributive property to multiply 3x+5 by 4x-7 and combine like terms.

$$12x^{2}-x-35=\left(12x+3\right)\left(x-16\right)$$

Use the distributive property to multiply 12x+3 by x-16 and combine like terms.

$$12x^{2}-x-35=12x^{2}-189x-48$$

Subtract 12x^{2} from both sides.

$$12x^{2}-x-35-12x^{2}=-189x-48$$

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

$$-x-35=-189x-48$$

Add 189x to both sides.

$$-x-35+189x=-48$$

Combine -x and 189x to get 188x.

$$188x-35=-48$$

Add 35 to both sides.

$$188x=-48+35$$

Add -48 and 35 to get -13.

$$188x=-13$$

Divide both sides by 188.

$$x=\frac{-13}{188}$$

Fraction \frac{-13}{188} can be rewritten as -\frac{13}{188} by extracting the negative sign.

$$x=-\frac{13}{188}$$