Solve x/2-x-1/3+1/4=7x+1/6

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

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps for Solving Linear Equation

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

$$6x-4\left(x-1\right)+3=2\left(7x+1\right)$$

Use the distributive property to multiply -4 by x-1.

$$6x-4x+4+3=2\left(7x+1\right)$$

Combine 6x and -4x to get 2x.

$$2x+4+3=2\left(7x+1\right)$$

Add 4 and 3 to get 7.

$$2x+7=2\left(7x+1\right)$$

Use the distributive property to multiply 2 by 7x+1.

$$2x+7=14x+2$$

Subtract 14x from both sides.

$$2x+7-14x=2$$

Combine 2x and -14x to get -12x.

$$-12x+7=2$$

Subtract 7 from both sides.

$$-12x=2-7$$

Subtract 7 from 2 to get -5.

$$-12x=-5$$

Divide both sides by -12.

$$x=\frac{-5}{-12}$$

Fraction \frac{-5}{-12} can be simplified to \frac{5}{12} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{12}$$