Solve 4-7-3x/5=3-3-7x/10-x+1/2

$$4 - \frac { 7 - 3 x } { 5 } = 3 - \frac { 3 - 7 x } { 10 } - \frac { x + 1 } { 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10,2.

$$40-2\left(7-3x\right)=30-\left(3-7x\right)-5\left(x+1\right)$$

Use the distributive property to multiply -2 by 7-3x.

$$40-14+6x=30-\left(3-7x\right)-5\left(x+1\right)$$

Subtract 14 from 40 to get 26.

$$26+6x=30-\left(3-7x\right)-5\left(x+1\right)$$

To find the opposite of 3-7x, find the opposite of each term.

$$26+6x=30-3-\left(-7x\right)-5\left(x+1\right)$$

The opposite of -7x is 7x.

$$26+6x=30-3+7x-5\left(x+1\right)$$

Subtract 3 from 30 to get 27.

$$26+6x=27+7x-5\left(x+1\right)$$

Use the distributive property to multiply -5 by x+1.

$$26+6x=27+7x-5x-5$$

Combine 7x and -5x to get 2x.

$$26+6x=27+2x-5$$

Subtract 5 from 27 to get 22.

$$26+6x=22+2x$$

Subtract 2x from both sides.

$$26+6x-2x=22$$

Combine 6x and -2x to get 4x.

$$26+4x=22$$

Subtract 26 from both sides.

$$4x=22-26$$

Subtract 26 from 22 to get -4.

$$4x=-4$$

Divide both sides by 4.

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

Divide -4 by 4 to get -1.

$$x=-1$$