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

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

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 12, the least common multiple of 2,3,4.

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

Use the distributive property to multiply 6 by x-3.

$$6x-18+4\left(6-x\right)=12+3\left(1+2x\right)$$

Use the distributive property to multiply 4 by 6-x.

$$6x-18+24-4x=12+3\left(1+2x\right)$$

Add -18 and 24 to get 6.

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

Combine 6x and -4x to get 2x.

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

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

$$2x+6=12+3+6x$$

Add 12 and 3 to get 15.

$$2x+6=15+6x$$

Subtract 6x from both sides.

$$2x+6-6x=15$$

Combine 2x and -6x to get -4x.

$$-4x+6=15$$

Subtract 6 from both sides.

$$-4x=15-6$$

Subtract 6 from 15 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.

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