Solve (3-7x)/10-(7-3x)/5=1-(x+1)/3

$$( 3 - 7 x ) / 10 - ( 7 - 3 x ) / 5 = 1 - ( x + 1 ) / 3$$

Solve for x

$$x = \frac{53}{7} = 7\frac{4}{7} \approx 7.571428571$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 10,5,3.

$$3\left(3-7x\right)-6\left(7-3x\right)=30-10\left(x+1\right)$$

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

$$9-21x-6\left(7-3x\right)=30-10\left(x+1\right)$$

Use the distributive property to multiply -6 by 7-3x.

$$9-21x-42+18x=30-10\left(x+1\right)$$

Subtract 42 from 9 to get -33.

$$-33-21x+18x=30-10\left(x+1\right)$$

Combine -21x and 18x to get -3x.

$$-33-3x=30-10\left(x+1\right)$$

Use the distributive property to multiply -10 by x+1.

$$-33-3x=30-10x-10$$

Subtract 10 from 30 to get 20.

$$-33-3x=20-10x$$

Add 10x to both sides.

$$-33-3x+10x=20$$

Combine -3x and 10x to get 7x.

$$-33+7x=20$$

Add 33 to both sides.

$$7x=20+33$$

Add 20 and 33 to get 53.

$$7x=53$$

Divide both sides by 7.

$$x=\frac{53}{7}$$