Solve 0.2(x-2)-0.1(x+3)-2x-5/3+3=0

$$0.2(x-2)-0.1(x+3)- \frac{ 2x-5 }{ 3 } +3=0$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$0.6\left(x-2\right)-0.3\left(x+3\right)-\left(2x-5\right)+9=0$$

Use the distributive property to multiply 0.6 by x-2.

$$0.6x-1.2-0.3\left(x+3\right)-\left(2x-5\right)+9=0$$

Use the distributive property to multiply -0.3 by x+3.

$$0.6x-1.2-0.3x-0.9-\left(2x-5\right)+9=0$$

Combine 0.6x and -0.3x to get 0.3x.

$$0.3x-1.2-0.9-\left(2x-5\right)+9=0$$

Subtract 0.9 from -1.2 to get -2.1.

$$0.3x-2.1-\left(2x-5\right)+9=0$$

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

$$0.3x-2.1-2x-\left(-5\right)+9=0$$

The opposite of -5 is 5.

$$0.3x-2.1-2x+5+9=0$$

Combine 0.3x and -2x to get -1.7x.

$$-1.7x-2.1+5+9=0$$

Add -2.1 and 5 to get 2.9.

$$-1.7x+2.9+9=0$$

Add 2.9 and 9 to get 11.9.

$$-1.7x+11.9=0$$

Subtract 11.9 from both sides. Anything subtracted from zero gives its negation.

$$-1.7x=-11.9$$

Divide both sides by -1.7.

$$x=\frac{-11.9}{-1.7}$$

Expand \frac{-11.9}{-1.7} by multiplying both numerator and the denominator by 10.

$$x=\frac{-119}{-17}$$

Divide -119 by -17 to get 7.

$$x=7$$