Solve for x 3(1/6x+9)=1/2x-27

$3 (\frac{1}{6} x + 9) = \frac{1}{2} x - 27$

Step 1

Simplify $3 (\frac{1}{6} x + 9)$ .

Rewrite.

$0 + 0 + 3 (\frac{1}{6} x + 9) = \frac{1}{2} x - 27$

Simplify by adding zeros.

$3 (\frac{1}{6} x + 9) = \frac{1}{2} x - 27$

Combine $\frac{1}{6}$ and $x$ .

$3 (\frac{x}{6} + 9) = \frac{1}{2} x - 27$

Apply the distributive property.

$3 \frac{x}{6} + 3 \cdot 9 = \frac{1}{2} x - 27$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$3 \frac{x}{3 (2)} + 3 \cdot 9 = \frac{1}{2} x - 27$

Cancel the common factor.

$3 \frac{x}{3 \cdot 2} + 3 \cdot 9 = \frac{1}{2} x - 27$

Rewrite the expression.

$\frac{x}{2} + 3 \cdot 9 = \frac{1}{2} x - 27$

Multiply $3$ by $9$ .

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

Step 2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + 27 = \frac{x}{2} - 27$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{x}{2} + 27 - \frac{x}{2} = - 27$

Combine the opposite terms in $\frac{x}{2} + 27 - \frac{x}{2}$ .

Subtract $\frac{x}{2}$ from $\frac{x}{2}$ .

$0 + 27 = - 27$

Add $0$ and $27$ .

$27 = - 27$

Step 4

Since $27 \neq - 27$ , there are no solutions.

No solution