Solve 2x+1/4=10x+1/6-2x-1/3

$$\frac { 2 x + 1 } { 4 } = \frac { 10 x + 1 } { 6 } - \frac { 2 x - 1 } { 3 }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

$$3\left(2x+1\right)=2\left(10x+1\right)-4\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x+1.

$$6x+3=2\left(10x+1\right)-4\left(2x-1\right)$$

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

$$6x+3=20x+2-4\left(2x-1\right)$$

Use the distributive property to multiply -4 by 2x-1.

$$6x+3=20x+2-8x+4$$

Combine 20x and -8x to get 12x.

$$6x+3=12x+2+4$$

Add 2 and 4 to get 6.

$$6x+3=12x+6$$

Subtract 12x from both sides.

$$6x+3-12x=6$$

Combine 6x and -12x to get -6x.

$$-6x+3=6$$

Subtract 3 from both sides.

$$-6x=6-3$$

Subtract 3 from 6 to get 3.

$$-6x=3$$

Divide both sides by -6.

$$x=\frac{3}{-6}$$

Reduce the fraction \frac{3}{-6} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{2}$$