Solve 7x-1/3/-4-5x-3/4/3=frac{2x-1,5}{-6}+frac{5x-1frac{1}{6}}{2}

$$\frac { 7 x - \frac { 1 } { 3 } } { - 4 } - \frac { 5 x - \frac { 3 } { 4 } } { 3 } = \frac { 2 x - 1,5 } { - 6 } + \frac { 5 x - 1 \frac { 1 } { 6 } } { 2 }$$

Solve for x

$$x=\frac{8}{67}\approx 0,119402985$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of -4;3;-6;2.

$$-3\left(7x-\frac{1}{3}\right)-4\left(5x-\frac{3}{4}\right)=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Use the distributive property to multiply -3 by 7x-\frac{1}{3}.

$$-21x-3\left(-\frac{1}{3}\right)-4\left(5x-\frac{3}{4}\right)=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Multiply -3 times -\frac{1}{3}.

$$-21x+1-4\left(5x-\frac{3}{4}\right)=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Use the distributive property to multiply -4 by 5x-\frac{3}{4}.

$$-21x+1-20x-4\left(-\frac{3}{4}\right)=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Multiply -4 times -\frac{3}{4}.

$$-21x+1-20x+3=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Combine -21x and -20x to get -41x.

$$-41x+1+3=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Add 1 and 3 to get 4.

$$-41x+4=-2\left(2x-1,5\right)+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Use the distributive property to multiply -2 by 2x-1,5.

$$-41x+4=-4x+3+6\left(5x-\frac{1\times 6+1}{6}\right)$$

Multiply 1 and 6 to get 6.

$$-41x+4=-4x+3+6\left(5x-\frac{6+1}{6}\right)$$

Add 6 and 1 to get 7.

$$-41x+4=-4x+3+6\left(5x-\frac{7}{6}\right)$$

Use the distributive property to multiply 6 by 5x-\frac{7}{6}.

$$-41x+4=-4x+3+30x+6\left(-\frac{7}{6}\right)$$

Cancel out 6 and 6.

$$-41x+4=-4x+3+30x-7$$

Combine -4x and 30x to get 26x.

$$-41x+4=26x+3-7$$

Subtract 7 from 3 to get -4.

$$-41x+4=26x-4$$

Subtract 26x from both sides.

$$-41x+4-26x=-4$$

Combine -41x and -26x to get -67x.

$$-67x+4=-4$$

Subtract 4 from both sides.

$$-67x=-4-4$$

Subtract 4 from -4 to get -8.

$$-67x=-8$$

Divide both sides by -67.

$$x=\frac{-8}{-67}$$

Fraction \frac{-8}{-67} can be simplified to \frac{8}{67} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{8}{67}$$