Solve x-4/2+x+3/6-x-6/3=1+x-7/2

$$\frac { x - 4 } { 2 } + \frac { x + 3 } { 6 } - \frac { x - 6 } { 3 } = 1 + \frac { x - 7 } { 2 }$$

Solve for x

$$x=18$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$3\left(x-4\right)+x+3-2\left(x-6\right)=6+3\left(x-7\right)$$

Use the distributive property to multiply 3 by x-4.

$$3x-12+x+3-2\left(x-6\right)=6+3\left(x-7\right)$$

Combine 3x and x to get 4x.

$$4x-12+3-2\left(x-6\right)=6+3\left(x-7\right)$$

Add -12 and 3 to get -9.

$$4x-9-2\left(x-6\right)=6+3\left(x-7\right)$$

Use the distributive property to multiply -2 by x-6.

$$4x-9-2x+12=6+3\left(x-7\right)$$

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

$$2x-9+12=6+3\left(x-7\right)$$

Add -9 and 12 to get 3.

$$2x+3=6+3\left(x-7\right)$$

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

$$2x+3=6+3x-21$$

Subtract 21 from 6 to get -15.

$$2x+3=-15+3x$$

Subtract 3x from both sides.

$$2x+3-3x=-15$$

Combine 2x and -3x to get -x.

$$-x+3=-15$$

Subtract 3 from both sides.

$$-x=-15-3$$

Subtract 3 from -15 to get -18.

$$-x=-18$$

Multiply both sides by -1.

$$x=18$$