Solve 1-6-x/3/2+x-x/2-frac{3+x/4}{2}=3

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

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

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

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

Since \frac{2x}{4} and \frac{3+x}{4} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Combine like terms in 2x-3-x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{6-x}{3} times \frac{4}{4}. Multiply \frac{x-3}{4} times \frac{3}{3}.

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

Since -\frac{4\left(6-x\right)}{12} and \frac{3\left(x-3\right)}{12} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in -4\left(6-x\right)-3\left(x-3\right).

$$1+\frac{-24+4x-3x+9}{12}+2x=6$$

Combine like terms in -24+4x-3x+9.

$$1+\frac{-15+x}{12}+2x=6$$

Divide each term of -15+x by 12 to get -\frac{5}{4}+\frac{1}{12}x.

$$1-\frac{5}{4}+\frac{1}{12}x+2x=6$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}-\frac{5}{4}+\frac{1}{12}x+2x=6$$

Since \frac{4}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-5}{4}+\frac{1}{12}x+2x=6$$

Subtract 5 from 4 to get -1.

$$-\frac{1}{4}+\frac{1}{12}x+2x=6$$

Combine \frac{1}{12}x and 2x to get \frac{25}{12}x.

$$-\frac{1}{4}+\frac{25}{12}x=6$$

Add \frac{1}{4} to both sides.

$$\frac{25}{12}x=6+\frac{1}{4}$$

Convert 6 to fraction \frac{24}{4}.

$$\frac{25}{12}x=\frac{24}{4}+\frac{1}{4}$$

Since \frac{24}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{25}{12}x=\frac{24+1}{4}$$

Add 24 and 1 to get 25.

$$\frac{25}{12}x=\frac{25}{4}$$

Multiply both sides by \frac{12}{25}, the reciprocal of \frac{25}{12}.

$$x=\frac{25}{4}\times \frac{12}{25}$$

Multiply \frac{25}{4} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{25\times 12}{4\times 25}$$

Cancel out 25 in both numerator and denominator.

$$x=\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x=3$$