Solve x+1/2-0.2x-1/0.1=1

$$\frac { x + 1 } { 2 } - \frac { 0.2 x - 1 } { 0.1 } = 1$$

Solve for x

$$x = \frac{19}{3} = 6\frac{1}{3} \approx 6.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$x+1-2\times \frac{0.2x-1}{0.1}=2$$

Divide each term of 0.2x-1 by 0.1 to get \frac{0.2x}{0.1}+\frac{-1}{0.1}.

$$x+1-2\left(\frac{0.2x}{0.1}+\frac{-1}{0.1}\right)=2$$

Divide 0.2x by 0.1 to get 2x.

$$x+1-2\left(2x+\frac{-1}{0.1}\right)=2$$

Expand \frac{-1}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$x+1-2\left(2x-10\right)=2$$

Use the distributive property to multiply -2 by 2x-10.

$$x+1-4x+20=2$$

Combine x and -4x to get -3x.

$$-3x+1+20=2$$

Add 1 and 20 to get 21.

$$-3x+21=2$$

Subtract 21 from both sides.

$$-3x=2-21$$

Subtract 21 from 2 to get -19.

$$-3x=-19$$

Divide both sides by -3.

$$x=\frac{-19}{-3}$$

Fraction \frac{-19}{-3} can be simplified to \frac{19}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{19}{3}$$