Solve 1-8x/4+3x=2+16x/3-6x

$$\frac{ 1-8x }{ 4+3x } = \frac{ 2+16x }{ 3-6x }$$

Solve for x

$$x=-\frac{1}{20}=-0.05$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{4}{3},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 3\left(2x-1\right)\left(3x+4\right), the least common multiple of 4+3x,3-6x.

$$\left(6x-3\right)\left(1-8x\right)=\left(-4-3x\right)\left(2+16x\right)$$

Use the distributive property to multiply 6x-3 by 1-8x and combine like terms.

$$30x-48x^{2}-3=\left(-4-3x\right)\left(2+16x\right)$$

Use the distributive property to multiply -4-3x by 2+16x and combine like terms.

$$30x-48x^{2}-3=-8-70x-48x^{2}$$

Add 70x to both sides.

$$30x-48x^{2}-3+70x=-8-48x^{2}$$

Combine 30x and 70x to get 100x.

$$100x-48x^{2}-3=-8-48x^{2}$$

Add 48x^{2} to both sides.

$$100x-48x^{2}-3+48x^{2}=-8$$

Combine -48x^{2} and 48x^{2} to get 0.

$$100x-3=-8$$

Add 3 to both sides.

$$100x=-8+3$$

Add -8 and 3 to get -5.

$$100x=-5$$

Divide both sides by 100.

$$x=\frac{-5}{100}$$

Reduce the fraction \frac{-5}{100} to lowest terms by extracting and canceling out 5.

$$x=-\frac{1}{20}$$