Solve x+1/6=2x-1/3-1-4x/5

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,3,5.

$$30x+5=10\left(2x-1\right)-6\left(1-4x\right)$$

Use the distributive property to multiply 10 by 2x-1.

$$30x+5=20x-10-6\left(1-4x\right)$$

Use the distributive property to multiply -6 by 1-4x.

$$30x+5=20x-10-6+24x$$

Subtract 6 from -10 to get -16.

$$30x+5=20x-16+24x$$

Combine 20x and 24x to get 44x.

$$30x+5=44x-16$$

Subtract 44x from both sides.

$$30x+5-44x=-16$$

Combine 30x and -44x to get -14x.

$$-14x+5=-16$$

Subtract 5 from both sides.

$$-14x=-16-5$$

Subtract 5 from -16 to get -21.

$$-14x=-21$$

Divide both sides by -14.

$$x=\frac{-21}{-14}$$

Reduce the fraction \frac{-21}{-14} to lowest terms by extracting and canceling out -7.

$$x=\frac{3}{2}$$