Solve for x x/2+1=1/4x-6

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

Step 1

Combine $\frac{1}{4}$ and $x$ .

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

Step 2

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

Subtract $\frac{x}{4}$ from both sides of the equation.

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

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Subtract $x$ from $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Subtract $x$ from $2 \cdot x$ .

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

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$\frac{x}{4} = - 6 - 1$

Subtract $1$ from $- 6$ .

$\frac{x}{4} = - 7$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot - 7$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot - 7$

Rewrite the expression.

$x = 4 \cdot - 7$

Simplify the right side.

Multiply $4$ by $- 7$ .

$x = - 28$