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

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

Solve for x

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,3,2.

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

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

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

Combine x and -2x to get -x.

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

Subtract 4 from -2 to get -6.

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

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

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

Subtract 3 from 6 to get 3.

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

Subtract 3x from both sides.

$$-x-6-3x=3$$

Combine -x and -3x to get -4x.

$$-4x-6=3$$

Add 6 to both sides.

$$-4x=3+6$$

Add 3 and 6 to get 9.

$$-4x=9$$

Divide both sides by -4.

$$x=\frac{9}{-4}$$

Fraction \frac{9}{-4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$x=-\frac{9}{4}$$