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

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

Solve for x

$$x=-\frac{1}{7}\approx -0.142857143$$

Steps for Solving Linear Equation

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

$$3\left(5x-1\right)=6\left(3x+1\right)-4\left(2-x\right)$$

Use the distributive property to multiply 3 by 5x-1.

$$15x-3=6\left(3x+1\right)-4\left(2-x\right)$$

Use the distributive property to multiply 6 by 3x+1.

$$15x-3=18x+6-4\left(2-x\right)$$

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

$$15x-3=18x+6-8+4x$$

Subtract 8 from 6 to get -2.

$$15x-3=18x-2+4x$$

Combine 18x and 4x to get 22x.

$$15x-3=22x-2$$

Subtract 22x from both sides.

$$15x-3-22x=-2$$

Combine 15x and -22x to get -7x.

$$-7x-3=-2$$

Add 3 to both sides.

$$-7x=-2+3$$

Add -2 and 3 to get 1.

$$-7x=1$$

Divide both sides by -7.

$$x=\frac{1}{-7}$$

Fraction \frac{1}{-7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$x=-\frac{1}{7}$$