Solve 5x-1.5/0.5-3x-0.4/0.2=1.2-x/0.1

$$\frac { 5 x - 1.5 } { 0.5 } - \frac { 3 x - 0.4 } { 0.2 } = \frac { 1.2 - x } { 0.1 }$$

Solve for x

$$x=2.6$$

Steps for Solving Linear Equation

Divide each term of 5x-1.5 by 0.5 to get \frac{5x}{0.5}+\frac{-1.5}{0.5}.

$$\frac{5x}{0.5}+\frac{-1.5}{0.5}-\frac{3x-0.4}{0.2}=\frac{1.2-x}{0.1}$$

Divide 5x by 0.5 to get 10x.

$$10x+\frac{-1.5}{0.5}-\frac{3x-0.4}{0.2}=\frac{1.2-x}{0.1}$$

Expand \frac{-1.5}{0.5} by multiplying both numerator and the denominator by 10.

$$10x+\frac{-15}{5}-\frac{3x-0.4}{0.2}=\frac{1.2-x}{0.1}$$

Divide -15 by 5 to get -3.

$$10x-3-\frac{3x-0.4}{0.2}=\frac{1.2-x}{0.1}$$

Divide each term of 3x-0.4 by 0.2 to get \frac{3x}{0.2}+\frac{-0.4}{0.2}.

$$10x-3-\left(\frac{3x}{0.2}+\frac{-0.4}{0.2}\right)=\frac{1.2-x}{0.1}$$

Divide 3x by 0.2 to get 15x.

$$10x-3-\left(15x+\frac{-0.4}{0.2}\right)=\frac{1.2-x}{0.1}$$

Expand \frac{-0.4}{0.2} by multiplying both numerator and the denominator by 10.

$$10x-3-\left(15x+\frac{-4}{2}\right)=\frac{1.2-x}{0.1}$$

Divide -4 by 2 to get -2.

$$10x-3-\left(15x-2\right)=\frac{1.2-x}{0.1}$$

To find the opposite of 15x-2, find the opposite of each term.

$$10x-3-15x-\left(-2\right)=\frac{1.2-x}{0.1}$$

The opposite of -2 is 2.

$$10x-3-15x+2=\frac{1.2-x}{0.1}$$

Combine 10x and -15x to get -5x.

$$-5x-3+2=\frac{1.2-x}{0.1}$$

Add -3 and 2 to get -1.

$$-5x-1=\frac{1.2-x}{0.1}$$

Divide each term of 1.2-x by 0.1 to get \frac{1.2}{0.1}+\frac{-x}{0.1}.

$$-5x-1=\frac{1.2}{0.1}+\frac{-x}{0.1}$$

Expand \frac{1.2}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$-5x-1=12+\frac{-x}{0.1}$$

Divide -x by 0.1 to get -10x.

$$-5x-1=12-10x$$

Add 10x to both sides.

$$-5x-1+10x=12$$

Combine -5x and 10x to get 5x.

$$5x-1=12$$

Add 1 to both sides.

$$5x=12+1$$

Add 12 and 1 to get 13.

$$5x=13$$

Divide both sides by 5.

$$x=\frac{13}{5}$$