Solve for x x/2+2=-3x+9

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

Step 1

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

Add $3 x$ to both sides of the equation.

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

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $3 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x + 3 x \cdot 2$ .

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $3 x \cdot 2$ .

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

Factor $x$ out of $x \cdot 1 + x (3 \cdot 2)$ .

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

Multiply $3$ by $2$ .

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

Add $1$ and $6$ .

$\frac{x \cdot 7}{2} + 2 = 9$

Move $7$ to the left of $x$ .

$\frac{7 x}{2} + 2 = 9$

Step 2

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

Subtract $2$ from both sides of the equation.

$\frac{7 x}{2} = 9 - 2$

Subtract $2$ from $9$ .

$\frac{7 x}{2} = 7$

Step 3

Multiply both sides of the equation by $\frac{2}{7}$ .

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 7$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{7} \cdot \frac{7 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{7} \cdot \frac{7 x}{2} = \frac{2}{7} \cdot 7$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 7$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{2}{7} \cdot 7$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{2}{7} \cdot 7$

Rewrite the expression.

$x = \frac{2}{7} \cdot 7$

Simplify the right side.

Cancel the common factor of $7$ .

Cancel the common factor.

$x = \frac{2}{7} \cdot 7$

Rewrite the expression.

$x = 2$

Solve for x x/2+2=-3x+9

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