Solve 2x-7/2-3x+1/5+x=5-x+6/2

$$\frac{ 2x-7 }{ 2 } - \frac{ 3x+1 }{ 5 } +x = 5- \frac{ x+6 }{ 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

$$5\left(2x-7\right)-2\left(3x+1\right)+10x=50-5\left(x+6\right)$$

Use the distributive property to multiply 5 by 2x-7.

$$10x-35-2\left(3x+1\right)+10x=50-5\left(x+6\right)$$

Use the distributive property to multiply -2 by 3x+1.

$$10x-35-6x-2+10x=50-5\left(x+6\right)$$

Combine 10x and -6x to get 4x.

$$4x-35-2+10x=50-5\left(x+6\right)$$

Subtract 2 from -35 to get -37.

$$4x-37+10x=50-5\left(x+6\right)$$

Combine 4x and 10x to get 14x.

$$14x-37=50-5\left(x+6\right)$$

Use the distributive property to multiply -5 by x+6.

$$14x-37=50-5x-30$$

Subtract 30 from 50 to get 20.

$$14x-37=20-5x$$

Add 5x to both sides.

$$14x-37+5x=20$$

Combine 14x and 5x to get 19x.

$$19x-37=20$$

Add 37 to both sides.

$$19x=20+37$$

Add 20 and 37 to get 57.

$$19x=57$$

Divide both sides by 19.

$$x=\frac{57}{19}$$

Divide 57 by 19 to get 3.

$$x=3$$