Solve x/0.5-0.4x-0.6/0.2=2(-x+3)

$$\frac { x } { 0.5 } - \frac { 0.4 x - 0.6 } { 0.2 } = 2 ( - x + 3 )$$

Solve for x

$$x=1.5$$

Steps for Solving Linear Equation

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

$$\frac{x}{0.5}-\frac{0.4x-0.6}{0.2}=2\left(-x\right)+6$$

Divide each term of 0.4x-0.6 by 0.2 to get \frac{0.4x}{0.2}+\frac{-0.6}{0.2}.

$$\frac{x}{0.5}-\left(\frac{0.4x}{0.2}+\frac{-0.6}{0.2}\right)=2\left(-x\right)+6$$

Divide 0.4x by 0.2 to get 2x.

$$\frac{x}{0.5}-\left(2x+\frac{-0.6}{0.2}\right)=2\left(-x\right)+6$$

Expand \frac{-0.6}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{x}{0.5}-\left(2x+\frac{-6}{2}\right)=2\left(-x\right)+6$$

Divide -6 by 2 to get -3.

$$\frac{x}{0.5}-\left(2x-3\right)=2\left(-x\right)+6$$

To find the opposite of 2x-3, find the opposite of each term.

$$\frac{x}{0.5}-2x-\left(-3\right)=2\left(-x\right)+6$$

The opposite of -3 is 3.

$$\frac{x}{0.5}-2x+3=2\left(-x\right)+6$$

Subtract 2\left(-x\right) from both sides.

$$\frac{x}{0.5}-2x+3-2\left(-x\right)=6$$

Multiply -1 and 2 to get -2.

$$\frac{x}{0.5}-2x+3-2\left(-1\right)x=6$$

Multiply -2 and -1 to get 2.

$$\frac{x}{0.5}-2x+3+2x=6$$

Combine -2x and 2x to get 0.

$$\frac{x}{0.5}+3=6$$

Subtract 3 from both sides.

$$\frac{x}{0.5}=6-3$$

Subtract 3 from 6 to get 3.

$$\frac{x}{0.5}=3$$

Multiply both sides by 0.5.

$$x=3\times 0.5$$

Multiply 3 and 0.5 to get 1.5.

$$x=1.5$$