Solve x+3/2=4/1-x+1/4-2-5x/3

$$\frac { x + 3 } { 2 } = \frac { 4 } { 1 } - \frac { x + 1 } { 4 } - \frac { 2 - 5 x } { 3 }$$

Solve for x

$$x = -\frac{19}{11} = -1\frac{8}{11} \approx -1.727272727$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,4,3.

$$6\left(x+3\right)=12\times 4-3\left(x+1\right)-4\left(2-5x\right)$$

Use the distributive property to multiply 6 by x+3.

$$6x+18=12\times 4-3\left(x+1\right)-4\left(2-5x\right)$$

Multiply 12 and 4 to get 48.

$$6x+18=48-3\left(x+1\right)-4\left(2-5x\right)$$

Use the distributive property to multiply -3 by x+1.

$$6x+18=48-3x-3-4\left(2-5x\right)$$

Subtract 3 from 48 to get 45.

$$6x+18=45-3x-4\left(2-5x\right)$$

Use the distributive property to multiply -4 by 2-5x.

$$6x+18=45-3x-8+20x$$

Subtract 8 from 45 to get 37.

$$6x+18=37-3x+20x$$

Combine -3x and 20x to get 17x.

$$6x+18=37+17x$$

Subtract 17x from both sides.

$$6x+18-17x=37$$

Combine 6x and -17x to get -11x.

$$-11x+18=37$$

Subtract 18 from both sides.

$$-11x=37-18$$

Subtract 18 from 37 to get 19.

$$-11x=19$$

Divide both sides by -11.

$$x=\frac{19}{-11}$$

Fraction \frac{19}{-11} can be rewritten as -\frac{19}{11} by extracting the negative sign.

$$x=-\frac{19}{11}$$