Solve x-3/4x+9/2+9-4x=6

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Combine x and -\frac{3}{4}x to get \frac{1}{4}x.

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

Convert 9 to fraction \frac{18}{2}.

$$\frac{1}{4}x+\frac{9}{2}+\frac{18}{2}-4x=6$$

Since \frac{9}{2} and \frac{18}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}x+\frac{9+18}{2}-4x=6$$

Add 9 and 18 to get 27.

$$\frac{1}{4}x+\frac{27}{2}-4x=6$$

Combine \frac{1}{4}x and -4x to get -\frac{15}{4}x.

$$-\frac{15}{4}x+\frac{27}{2}=6$$

Subtract \frac{27}{2} from both sides.

$$-\frac{15}{4}x=6-\frac{27}{2}$$

Convert 6 to fraction \frac{12}{2}.

$$-\frac{15}{4}x=\frac{12}{2}-\frac{27}{2}$$

Since \frac{12}{2} and \frac{27}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{15}{4}x=\frac{12-27}{2}$$

Subtract 27 from 12 to get -15.

$$-\frac{15}{4}x=-\frac{15}{2}$$

Multiply both sides by -\frac{4}{15}, the reciprocal of -\frac{15}{4}.

$$x=-\frac{15}{2}\left(-\frac{4}{15}\right)$$

Multiply -\frac{15}{2} times -\frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-15\left(-4\right)}{2\times 15}$$

Do the multiplications in the fraction \frac{-15\left(-4\right)}{2\times 15}.

$$x=\frac{60}{30}$$

Divide 60 by 30 to get 2.

$$x=2$$