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

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply -3 by 2x+4.

$$2x+4-6x-12=3x+7-12x$$

Combine 2x and -6x to get -4x.

$$-4x+4-12=3x+7-12x$$

Subtract 12 from 4 to get -8.

$$-4x-8=3x+7-12x$$

Combine 3x and -12x to get -9x.

$$-4x-8=-9x+7$$

Add 9x to both sides.

$$-4x-8+9x=7$$

Combine -4x and 9x to get 5x.

$$5x-8=7$$

Add 8 to both sides.

$$5x=7+8$$

Add 7 and 8 to get 15.

$$5x=15$$

Divide both sides by 5.

$$x=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x=3$$