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

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

Solve for x

$$x=-\frac{83}{230}\approx -0.360869565$$

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.

$$12x^{2}+41x+35=\left(12x+3\right)\left(x-16\right)$$

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

$$12x^{2}+41x+35=12x^{2}-189x-48$$

Subtract 12x^{2} from both sides.

$$12x^{2}+41x+35-12x^{2}=-189x-48$$

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

$$41x+35=-189x-48$$

Add 189x to both sides.

$$41x+35+189x=-48$$

Combine 41x and 189x to get 230x.

$$230x+35=-48$$

Subtract 35 from both sides.

$$230x=-48-35$$

Subtract 35 from -48 to get -83.

$$230x=-83$$

Divide both sides by 230.

$$x=\frac{-83}{230}$$

Fraction \frac{-83}{230} can be rewritten as -\frac{83}{230} by extracting the negative sign.

$$x=-\frac{83}{230}$$