Solve x/4+9x/4+3x/2+30=x

$$\frac{ x }{ 4 } + \frac{ 9x }{ 4 } + \frac{ 3x }{ 2 } +30 = x$$

Solve for x

$$x=-10$$

Steps for Solving Linear Equation

Since \frac{x}{4} and \frac{9x}{4} have the same denominator, add them by adding their numerators.

$$\frac{x+9x}{4}+\frac{3x}{2}+30=x$$

Combine like terms in x+9x.

$$\frac{10x}{4}+\frac{3x}{2}+30=x$$

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

$$\frac{10x}{4}+\frac{2\times 3x}{4}+30=x$$

Since \frac{10x}{4} and \frac{2\times 3x}{4} have the same denominator, add them by adding their numerators.

$$\frac{10x+2\times 3x}{4}+30=x$$

Do the multiplications in 10x+2\times 3x.

$$\frac{10x+6x}{4}+30=x$$

Combine like terms in 10x+6x.

$$\frac{16x}{4}+30=x$$

Divide 16x by 4 to get 4x.

$$4x+30=x$$

Subtract x from both sides.

$$4x+30-x=0$$

Combine 4x and -x to get 3x.

$$3x+30=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$3x=-30$$

Divide both sides by 3.

$$x=\frac{-30}{3}$$

Divide -30 by 3 to get -10.

$$x=-10$$