Solve x+5/2+3-2x/4=x-7+x/6

$$\frac { x + 5 } { 2 } + \frac { 3 - 2 x } { 4 } = x - \frac { 7 + x } { 6 }$$

Solve for x

$$x = \frac{53}{10} = 5\frac{3}{10} = 5.3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,4,6.

$$6\left(x+5\right)+3\left(3-2x\right)=12x-2\left(7+x\right)$$

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

$$6x+30+3\left(3-2x\right)=12x-2\left(7+x\right)$$

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

$$6x+30+9-6x=12x-2\left(7+x\right)$$

Add 30 and 9 to get 39.

$$6x+39-6x=12x-2\left(7+x\right)$$

Combine 6x and -6x to get 0.

$$39=12x-2\left(7+x\right)$$

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

$$39=12x-14-2x$$

Combine 12x and -2x to get 10x.

$$39=10x-14$$

Swap sides so that all variable terms are on the left hand side.

$$10x-14=39$$

Add 14 to both sides.

$$10x=39+14$$

Add 39 and 14 to get 53.

$$10x=53$$

Divide both sides by 10.

$$x=\frac{53}{10}$$