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

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

Solve for x

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Steps for Solving Linear Equation

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

$$2\left(x+1\right)-4\left(x-4\right)=24+3$$

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

$$2x+2-4\left(x-4\right)=24+3$$

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

$$2x+2-4x+16=24+3$$

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

$$-2x+2+16=24+3$$

Add 2 and 16 to get 18.

$$-2x+18=24+3$$

Add 24 and 3 to get 27.

$$-2x+18=27$$

Subtract 18 from both sides.

$$-2x=27-18$$

Subtract 18 from 27 to get 9.

$$-2x=9$$

Divide both sides by -2.

$$x=\frac{9}{-2}$$

Fraction \frac{9}{-2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$x=-\frac{9}{2}$$