Solve (g)1/3-[3/4-x-3/2]=x-3/6-x

$$( g ) \frac { 1 } { 3 } - [ \frac { 3 } { 4 } - \frac { x - 3 } { 2 } ] = \frac { x - 3 } { 6 } - x$$

Solve for g

$$g=\frac{21}{4}-4x$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,2,6.

$$12g\times \frac{1}{3}-12\left(\frac{3}{4}-\frac{x-3}{2}\right)=2\left(x-3\right)-12x$$

Multiply 12 and \frac{1}{3} to get 4.

$$4g-12\left(\frac{3}{4}-\frac{x-3}{2}\right)=2\left(x-3\right)-12x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{x-3}{2} times \frac{2}{2}.

$$4g-12\left(\frac{3}{4}-\frac{2\left(x-3\right)}{4}\right)=2\left(x-3\right)-12x$$

Since \frac{3}{4} and \frac{2\left(x-3\right)}{4} have the same denominator, subtract them by subtracting their numerators.

$$4g-12\times \frac{3-2\left(x-3\right)}{4}=2\left(x-3\right)-12x$$

Do the multiplications in 3-2\left(x-3\right).

$$4g-12\times \frac{3-2x+6}{4}=2\left(x-3\right)-12x$$

Combine like terms in 3-2x+6.

$$4g-12\times \frac{9-2x}{4}=2\left(x-3\right)-12x$$

Cancel out 4, the greatest common factor in 12 and 4.

$$4g-3\left(9-2x\right)=2\left(x-3\right)-12x$$

Use the distributive property to multiply -3 by 9-2x.

$$4g-27+6x=2\left(x-3\right)-12x$$

Use the distributive property to multiply 2 by x-3.

$$4g-27+6x=2x-6-12x$$

Combine 2x and -12x to get -10x.

$$4g-27+6x=-10x-6$$

Add 27 to both sides.

$$4g+6x=-10x-6+27$$

Add -6 and 27 to get 21.

$$4g+6x=-10x+21$$

Subtract 6x from both sides.

$$4g=-10x+21-6x$$

Combine -10x and -6x to get -16x.

$$4g=-16x+21$$

The equation is in standard form.

$$4g=21-16x$$

Divide both sides by 4.

$$\frac{4g}{4}=\frac{21-16x}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$g=\frac{21-16x}{4}$$

Divide -16x+21 by 4.

$$g=\frac{21}{4}-4x$$

Solve for x

$$x=-\frac{g}{4}+\frac{21}{16}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,2,6.

$$12g\times \frac{1}{3}-12\left(\frac{3}{4}-\frac{x-3}{2}\right)=2\left(x-3\right)-12x$$

Multiply 12 and \frac{1}{3} to get 4.

$$4g-12\left(\frac{3}{4}-\frac{x-3}{2}\right)=2\left(x-3\right)-12x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{x-3}{2} times \frac{2}{2}.

$$4g-12\left(\frac{3}{4}-\frac{2\left(x-3\right)}{4}\right)=2\left(x-3\right)-12x$$

Since \frac{3}{4} and \frac{2\left(x-3\right)}{4} have the same denominator, subtract them by subtracting their numerators.

$$4g-12\times \frac{3-2\left(x-3\right)}{4}=2\left(x-3\right)-12x$$

Do the multiplications in 3-2\left(x-3\right).

$$4g-12\times \frac{3-2x+6}{4}=2\left(x-3\right)-12x$$

Combine like terms in 3-2x+6.

$$4g-12\times \frac{9-2x}{4}=2\left(x-3\right)-12x$$

Cancel out 4, the greatest common factor in 12 and 4.

$$4g-3\left(9-2x\right)=2\left(x-3\right)-12x$$

Use the distributive property to multiply -3 by 9-2x.

$$4g-27+6x=2\left(x-3\right)-12x$$

Use the distributive property to multiply 2 by x-3.

$$4g-27+6x=2x-6-12x$$

Combine 2x and -12x to get -10x.

$$4g-27+6x=-10x-6$$

Add 10x to both sides.

$$4g-27+6x+10x=-6$$

Combine 6x and 10x to get 16x.

$$4g-27+16x=-6$$

Subtract 4g from both sides.

$$-27+16x=-6-4g$$

Add 27 to both sides.

$$16x=-6-4g+27$$

Add -6 and 27 to get 21.

$$16x=21-4g$$

Divide both sides by 16.

$$\frac{16x}{16}=\frac{21-4g}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x=\frac{21-4g}{16}$$

Divide 21-4g by 16.

$$x=-\frac{g}{4}+\frac{21}{16}$$