Solve 2x+1/4-10x+1/12=2x-1/3+1

$$\frac { 2 x + 1 } { 4 } - \frac { 10 x + 1 } { 12 } = \frac { 2 x - 1 } { 3 } + 1$$

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 4,12,3.

$$3\left(2x+1\right)-\left(10x+1\right)=4\left(2x-1\right)+12$$

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

$$6x+3-\left(10x+1\right)=4\left(2x-1\right)+12$$

To find the opposite of 10x+1, find the opposite of each term.

$$6x+3-10x-1=4\left(2x-1\right)+12$$

Combine 6x and -10x to get -4x.

$$-4x+3-1=4\left(2x-1\right)+12$$

Subtract 1 from 3 to get 2.

$$-4x+2=4\left(2x-1\right)+12$$

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

$$-4x+2=8x-4+12$$

Add -4 and 12 to get 8.

$$-4x+2=8x+8$$

Subtract 8x from both sides.

$$-4x+2-8x=8$$

Combine -4x and -8x to get -12x.

$$-12x+2=8$$

Subtract 2 from both sides.

$$-12x=8-2$$

Subtract 2 from 8 to get 6.

$$-12x=6$$

Divide both sides by -12.

$$x=\frac{6}{-12}$$

Reduce the fraction \frac{6}{-12} to lowest terms by extracting and canceling out 6.

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