Solve 7x+9/8-7-x/6-x=3-x/2-(7-x/3-frac{3+x}{4})

$$\frac { 7 x + 9 } { 8 } - \frac { 7 - x } { 6 } - x = \frac { 3 - x } { 2 } - ( \frac { 7 - x } { 3 } - \frac { 3 + x } { 4 } )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,6,2,3,4.

$$3\left(7x+9\right)-4\left(7-x\right)-24x=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Use the distributive property to multiply 3 by 7x+9.

$$21x+27-4\left(7-x\right)-24x=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Use the distributive property to multiply -4 by 7-x.

$$21x+27-28+4x-24x=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Subtract 28 from 27 to get -1.

$$21x-1+4x-24x=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Combine 21x and 4x to get 25x.

$$25x-1-24x=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Combine 25x and -24x to get x.

$$x-1=12\left(3-x\right)-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

Use the distributive property to multiply 12 by 3-x.

$$x-1=36-12x-24\left(\frac{7-x}{3}-\frac{3+x}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 4 is 12. Multiply \frac{7-x}{3} times \frac{4}{4}. Multiply \frac{3+x}{4} times \frac{3}{3}.

$$x-1=36-12x-24\left(\frac{4\left(7-x\right)}{12}-\frac{3\left(3+x\right)}{12}\right)$$

Since \frac{4\left(7-x\right)}{12} and \frac{3\left(3+x\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$x-1=36-12x-24\times \frac{4\left(7-x\right)-3\left(3+x\right)}{12}$$

Do the multiplications in 4\left(7-x\right)-3\left(3+x\right).

$$x-1=36-12x-24\times \frac{28-4x-9-3x}{12}$$

Combine like terms in 28-4x-9-3x.

$$x-1=36-12x-24\times \frac{19-7x}{12}$$

Cancel out 12, the greatest common factor in 24 and 12.

$$x-1=36-12x-2\left(19-7x\right)$$

Use the distributive property to multiply -2 by 19-7x.

$$x-1=36-12x-38+14x$$

Subtract 38 from 36 to get -2.

$$x-1=-2-12x+14x$$

Combine -12x and 14x to get 2x.

$$x-1=-2+2x$$

Subtract 2x from both sides.

$$x-1-2x=-2$$

Combine x and -2x to get -x.

$$-x-1=-2$$

Add 1 to both sides.

$$-x=-2+1$$

Add -2 and 1 to get -1.

$$-x=-1$$

Multiply both sides by -1.

$$x=1$$