Solve 0.2x-0.1/0.3-(1-x/4+1/12)=1

$$\frac { 0.2 x - 0.1 } { 0.3 } - ( \frac { 1 - x } { 4 } + \frac { 1 } { 12 } ) = 1$$

Solve for x

$$x = \frac{20}{11} = 1\frac{9}{11} \approx 1.818181818$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,12.

$$12\times \frac{0.2x-0.1}{0.3}-12\left(\frac{1-x}{4}+\frac{1}{12}\right)=12$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 12 is 12. Multiply \frac{1-x}{4} times \frac{3}{3}.

$$12\times \frac{0.2x-0.1}{0.3}-12\left(\frac{3\left(1-x\right)}{12}+\frac{1}{12}\right)=12$$

Since \frac{3\left(1-x\right)}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$12\times \frac{0.2x-0.1}{0.3}-12\times \frac{3\left(1-x\right)+1}{12}=12$$

Do the multiplications in 3\left(1-x\right)+1.

$$12\times \frac{0.2x-0.1}{0.3}-12\times \frac{3-3x+1}{12}=12$$

Combine like terms in 3-3x+1.

$$12\times \frac{0.2x-0.1}{0.3}-12\times \frac{4-3x}{12}=12$$

Express 12\times \frac{4-3x}{12} as a single fraction.

$$12\times \frac{0.2x-0.1}{0.3}-\frac{12\left(4-3x\right)}{12}=12$$

Cancel out 12 and 12.

$$12\times \frac{0.2x-0.1}{0.3}-\left(4-3x\right)=12$$

To find the opposite of 4-3x, find the opposite of each term.

$$12\times \frac{0.2x-0.1}{0.3}-4-\left(-3x\right)=12$$

The opposite of -3x is 3x.

$$12\times \frac{0.2x-0.1}{0.3}-4+3x=12$$

Divide each term of 0.2x-0.1 by 0.3 to get \frac{0.2x}{0.3}+\frac{-0.1}{0.3}.

$$12\left(\frac{0.2x}{0.3}+\frac{-0.1}{0.3}\right)-4+3x=12$$

Divide 0.2x by 0.3 to get \frac{2}{3}x.

$$12\left(\frac{2}{3}x+\frac{-0.1}{0.3}\right)-4+3x=12$$

Expand \frac{-0.1}{0.3} by multiplying both numerator and the denominator by 10.

$$12\left(\frac{2}{3}x+\frac{-1}{3}\right)-4+3x=12$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$12\left(\frac{2}{3}x-\frac{1}{3}\right)-4+3x=12$$

Use the distributive property to multiply 12 by \frac{2}{3}x-\frac{1}{3}.

$$8x+12\left(-\frac{1}{3}\right)-4+3x=12$$

Express 12\left(-\frac{1}{3}\right) as a single fraction.

$$8x+\frac{12\left(-1\right)}{3}-4+3x=12$$

Multiply 12 and -1 to get -12.

$$8x+\frac{-12}{3}-4+3x=12$$

Divide -12 by 3 to get -4.

$$8x-4-4+3x=12$$

Subtract 4 from -4 to get -8.

$$8x-8+3x=12$$

Combine 8x and 3x to get 11x.

$$11x-8=12$$

Add 8 to both sides.

$$11x=12+8$$

Add 12 and 8 to get 20.

$$11x=20$$

Divide both sides by 11.

$$x=\frac{20}{11}$$