Solve 6(x-7)-7(x-6)=x+6-(x-5)

$$6 ( x - 7 ) - 7 ( x - 6 ) = x + 6 - ( x - 5 )$$

Solve for x

$$x=-11$$

Steps for Solving Linear Equation

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

$$6x-42-7\left(x-6\right)=x+6-\left(x-5\right)$$

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

$$6x-42-7x+42=x+6-\left(x-5\right)$$

Combine 6x and -7x to get -x.

$$-x-42+42=x+6-\left(x-5\right)$$

Add -42 and 42 to get 0.

$$-x=x+6-\left(x-5\right)$$

To find the opposite of x-5, find the opposite of each term.

$$-x=x+6-x-\left(-5\right)$$

The opposite of -5 is 5.

$$-x=x+6-x+5$$

Combine x and -x to get 0.

$$-x=6+5$$

Add 6 and 5 to get 11.

$$-x=11$$

Multiply both sides by -1.

$$x=-11$$