Solve 3+2x/5+5x+2/4+3x=1+8x+7/20

$$\frac { 3 + 2 x } { 5 } + \frac { 5 x + 2 } { 4 + 3 x } = 1 + \frac { 8 x + 7 } { 20 }$$

Solve for x

$$x=\frac{4}{11}\approx 0.363636364$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 20\left(3x+4\right), the least common multiple of 5,4+3x,20.

$$\left(12x+16\right)\left(3+2x\right)+20\left(5x+2\right)=20\left(3x+4\right)+\left(3x+4\right)\left(8x+7\right)$$

Use the distributive property to multiply 12x+16 by 3+2x and combine like terms.

$$68x+24x^{2}+48+20\left(5x+2\right)=20\left(3x+4\right)+\left(3x+4\right)\left(8x+7\right)$$

Use the distributive property to multiply 20 by 5x+2.

$$68x+24x^{2}+48+100x+40=20\left(3x+4\right)+\left(3x+4\right)\left(8x+7\right)$$

Combine 68x and 100x to get 168x.

$$168x+24x^{2}+48+40=20\left(3x+4\right)+\left(3x+4\right)\left(8x+7\right)$$

Add 48 and 40 to get 88.

$$168x+24x^{2}+88=20\left(3x+4\right)+\left(3x+4\right)\left(8x+7\right)$$

Use the distributive property to multiply 20 by 3x+4.

$$168x+24x^{2}+88=60x+80+\left(3x+4\right)\left(8x+7\right)$$

Use the distributive property to multiply 3x+4 by 8x+7 and combine like terms.

$$168x+24x^{2}+88=60x+80+24x^{2}+53x+28$$

Combine 60x and 53x to get 113x.

$$168x+24x^{2}+88=113x+80+24x^{2}+28$$

Add 80 and 28 to get 108.

$$168x+24x^{2}+88=113x+108+24x^{2}$$

Subtract 113x from both sides.

$$168x+24x^{2}+88-113x=108+24x^{2}$$

Combine 168x and -113x to get 55x.

$$55x+24x^{2}+88=108+24x^{2}$$

Subtract 24x^{2} from both sides.

$$55x+24x^{2}+88-24x^{2}=108$$

Combine 24x^{2} and -24x^{2} to get 0.

$$55x+88=108$$

Subtract 88 from both sides.

$$55x=108-88$$

Subtract 88 from 108 to get 20.

$$55x=20$$

Divide both sides by 55.

$$x=\frac{20}{55}$$

Reduce the fraction \frac{20}{55} to lowest terms by extracting and canceling out 5.

$$x=\frac{4}{11}$$