Solve 4x-1.5/0.5-5x-0.8/0.2=1.2-x/0.1

$$\frac { 4 x - 1.5 } { 0.5 } - \frac { 5 x - 0.8 } { 0.2 } = \frac { 1.2 - x } { 0.1 }$$

Solve for x

$$x = -\frac{11}{7} = -1\frac{4}{7} \approx -1.571428571$$

Steps for Solving Linear Equation

Divide each term of 4x-1.5 by 0.5 to get \frac{4x}{0.5}+\frac{-1.5}{0.5}.

$$\frac{4x}{0.5}+\frac{-1.5}{0.5}-\frac{5x-0.8}{0.2}=\frac{1.2-x}{0.1}$$

Divide 4x by 0.5 to get 8x.

$$8x+\frac{-1.5}{0.5}-\frac{5x-0.8}{0.2}=\frac{1.2-x}{0.1}$$

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

$$8x+\frac{-15}{5}-\frac{5x-0.8}{0.2}=\frac{1.2-x}{0.1}$$

Divide -15 by 5 to get -3.

$$8x-3-\frac{5x-0.8}{0.2}=\frac{1.2-x}{0.1}$$

Divide each term of 5x-0.8 by 0.2 to get \frac{5x}{0.2}+\frac{-0.8}{0.2}.

$$8x-3-\left(\frac{5x}{0.2}+\frac{-0.8}{0.2}\right)=\frac{1.2-x}{0.1}$$

Divide 5x by 0.2 to get 25x.

$$8x-3-\left(25x+\frac{-0.8}{0.2}\right)=\frac{1.2-x}{0.1}$$

Expand \frac{-0.8}{0.2} by multiplying both numerator and the denominator by 10.

$$8x-3-\left(25x+\frac{-8}{2}\right)=\frac{1.2-x}{0.1}$$

Divide -8 by 2 to get -4.

$$8x-3-\left(25x-4\right)=\frac{1.2-x}{0.1}$$

To find the opposite of 25x-4, find the opposite of each term.

$$8x-3-25x-\left(-4\right)=\frac{1.2-x}{0.1}$$

The opposite of -4 is 4.

$$8x-3-25x+4=\frac{1.2-x}{0.1}$$

Combine 8x and -25x to get -17x.

$$-17x-3+4=\frac{1.2-x}{0.1}$$

Add -3 and 4 to get 1.

$$-17x+1=\frac{1.2-x}{0.1}$$

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

$$-17x+1=\frac{1.2}{0.1}+\frac{-x}{0.1}$$

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

$$-17x+1=12+\frac{-x}{0.1}$$

Divide -x by 0.1 to get -10x.

$$-17x+1=12-10x$$

Add 10x to both sides.

$$-17x+1+10x=12$$

Combine -17x and 10x to get -7x.

$$-7x+1=12$$

Subtract 1 from both sides.

$$-7x=12-1$$

Subtract 1 from 12 to get 11.

$$-7x=11$$

Divide both sides by -7.

$$x=\frac{11}{-7}$$

Fraction \frac{11}{-7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$x=-\frac{11}{7}$$