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

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

Solve for x

$$x = -\frac{27}{7} = -3\frac{6}{7} \approx -3.857142857$$

Steps for Solving Linear Equation

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

$$3\left(x-1\right)-2\times 4x-18=2x+6$$

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

$$3x-3-2\times 4x-18=2x+6$$

Multiply -2 and 4 to get -8.

$$3x-3-8x-18=2x+6$$

Combine 3x and -8x to get -5x.

$$-5x-3-18=2x+6$$

Subtract 18 from -3 to get -21.

$$-5x-21=2x+6$$

Subtract 2x from both sides.

$$-5x-21-2x=6$$

Combine -5x and -2x to get -7x.

$$-7x-21=6$$

Add 21 to both sides.

$$-7x=6+21$$

Add 6 and 21 to get 27.

$$-7x=27$$

Divide both sides by -7.

$$x=\frac{27}{-7}$$

Fraction \frac{27}{-7} can be rewritten as -\frac{27}{7} by extracting the negative sign.

$$x=-\frac{27}{7}$$