Solve x-7-x/3=x+6/7-7

$$x - \frac { 7 - x } { 3 } = \frac { x + 6 } { 7 } - 7$$

Solve for x

$$x = -\frac{16}{5} = -3\frac{1}{5} = -3.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 3,7.

$$21x-7\left(7-x\right)=3\left(x+6\right)-147$$

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

$$21x-49+7x=3\left(x+6\right)-147$$

Combine 21x and 7x to get 28x.

$$28x-49=3\left(x+6\right)-147$$

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

$$28x-49=3x+18-147$$

Subtract 147 from 18 to get -129.

$$28x-49=3x-129$$

Subtract 3x from both sides.

$$28x-49-3x=-129$$

Combine 28x and -3x to get 25x.

$$25x-49=-129$$

Add 49 to both sides.

$$25x=-129+49$$

Add -129 and 49 to get -80.

$$25x=-80$$

Divide both sides by 25.

$$x=\frac{-80}{25}$$

Reduce the fraction \frac{-80}{25} to lowest terms by extracting and canceling out 5.

$$x=-\frac{16}{5}$$