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

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

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 5 to get 10.

$$10x-12=-\left(5x-2\right)+3\left(3x+2\right)$$

To find the opposite of 5x-2, find the opposite of each term.

$$10x-12=-5x-\left(-2\right)+3\left(3x+2\right)$$

The opposite of -2 is 2.

$$10x-12=-5x+2+3\left(3x+2\right)$$

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

$$10x-12=-5x+2+9x+6$$

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

$$10x-12=4x+2+6$$

Add 2 and 6 to get 8.

$$10x-12=4x+8$$

Subtract 4x from both sides.

$$10x-12-4x=8$$

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

$$6x-12=8$$

Add 12 to both sides.

$$6x=8+12$$

Add 8 and 12 to get 20.

$$6x=20$$

Divide both sides by 6.

$$x=\frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{10}{3}$$