Solve x-1/5-x-2/8=x-1/4-x-2/10*frac{1}{20}

$$\frac { x - 1 } { 5 } - \frac { x - 2 } { 8 } = \frac { x - 1 } { 4 } - \frac { x - 2 } { 10 } \cdot \frac { 1 } { 20 }$$

Solve for x

$$x = \frac{29}{17} = 1\frac{12}{17} \approx 1.705882353$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 5,8,4,10,20.

$$8\left(x-1\right)-5\left(x-2\right)=10\left(x-1\right)-4\left(x-2\right)\times \frac{1}{20}$$

Use the distributive property to multiply 8 by x-1.

$$8x-8-5\left(x-2\right)=10\left(x-1\right)-4\left(x-2\right)\times \frac{1}{20}$$

Use the distributive property to multiply -5 by x-2.

$$8x-8-5x+10=10\left(x-1\right)-4\left(x-2\right)\times \frac{1}{20}$$

Combine 8x and -5x to get 3x.

$$3x-8+10=10\left(x-1\right)-4\left(x-2\right)\times \frac{1}{20}$$

Add -8 and 10 to get 2.

$$3x+2=10\left(x-1\right)-4\left(x-2\right)\times \frac{1}{20}$$

Use the distributive property to multiply 10 by x-1.

$$3x+2=10x-10-4\left(x-2\right)\times \frac{1}{20}$$

Multiply 4 and \frac{1}{20} to get \frac{4}{20}.

$$3x+2=10x-10-\frac{4}{20}\left(x-2\right)$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$3x+2=10x-10-\frac{1}{5}\left(x-2\right)$$

Use the distributive property to multiply -\frac{1}{5} by x-2.

$$3x+2=10x-10-\frac{1}{5}x-\frac{1}{5}\left(-2\right)$$

Express -\frac{1}{5}\left(-2\right) as a single fraction.

$$3x+2=10x-10-\frac{1}{5}x+\frac{-\left(-2\right)}{5}$$

Multiply -1 and -2 to get 2.

$$3x+2=10x-10-\frac{1}{5}x+\frac{2}{5}$$

Combine 10x and -\frac{1}{5}x to get \frac{49}{5}x.

$$3x+2=\frac{49}{5}x-10+\frac{2}{5}$$

Convert -10 to fraction -\frac{50}{5}.

$$3x+2=\frac{49}{5}x-\frac{50}{5}+\frac{2}{5}$$

Since -\frac{50}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$3x+2=\frac{49}{5}x+\frac{-50+2}{5}$$

Add -50 and 2 to get -48.

$$3x+2=\frac{49}{5}x-\frac{48}{5}$$

Subtract \frac{49}{5}x from both sides.

$$3x+2-\frac{49}{5}x=-\frac{48}{5}$$

Combine 3x and -\frac{49}{5}x to get -\frac{34}{5}x.

$$-\frac{34}{5}x+2=-\frac{48}{5}$$

Subtract 2 from both sides.

$$-\frac{34}{5}x=-\frac{48}{5}-2$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{34}{5}x=-\frac{48}{5}-\frac{10}{5}$$

Since -\frac{48}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{34}{5}x=\frac{-48-10}{5}$$

Subtract 10 from -48 to get -58.

$$-\frac{34}{5}x=-\frac{58}{5}$$

Multiply both sides by -\frac{5}{34}, the reciprocal of -\frac{34}{5}.

$$x=-\frac{58}{5}\left(-\frac{5}{34}\right)$$

Multiply -\frac{58}{5} times -\frac{5}{34} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-58\left(-5\right)}{5\times 34}$$

Do the multiplications in the fraction \frac{-58\left(-5\right)}{5\times 34}.

$$x=\frac{290}{170}$$

Reduce the fraction \frac{290}{170} to lowest terms by extracting and canceling out 10.

$$x=\frac{29}{17}$$