Solve for x 5x+1/2x=1/2x+10

$5 x + \frac{1}{2} x = \frac{1}{2} x + 10$

Step 1

Simplify $5 x + \frac{1}{2} x$ .

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

$5 x + \frac{x}{2} = \frac{1}{2} x + 10$

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x \cdot \frac{2}{2} + \frac{x}{2} = \frac{1}{2} x + 10$

Simplify terms.

Combine $5 x$ and $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{2} + \frac{x}{2} = \frac{1}{2} x + 10$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + x}{2} = \frac{1}{2} x + 10$

Simplify the numerator.

Factor $x$ out of $5 x \cdot 2 + x$ .

Factor $x$ out of $5 x \cdot 2$ .

$\frac{x (5 \cdot 2) + x}{2} = \frac{1}{2} x + 10$

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

$\frac{x (5 \cdot 2) + x^{1}}{2} = \frac{1}{2} x + 10$

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

$\frac{x (5 \cdot 2) + x \cdot 1}{2} = \frac{1}{2} x + 10$

Factor $x$ out of $x (5 \cdot 2) + x \cdot 1$ .

$\frac{x (5 \cdot 2 + 1)}{2} = \frac{1}{2} x + 10$

Multiply $5$ by $2$ .

$\frac{x (10 + 1)}{2} = \frac{1}{2} x + 10$

Add $10$ and $1$ .

$\frac{x \cdot 11}{2} = \frac{1}{2} x + 10$

Move $11$ to the left of $x$ .

$\frac{11 x}{2} = \frac{1}{2} x + 10$

Step 2

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

$\frac{11 x}{2} = \frac{x}{2} + 10$

Step 3

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

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

$\frac{11 x}{2} - \frac{x}{2} = 10$

Combine the numerators over the common denominator.

$\frac{11 x - x}{2} = 10$

Subtract $x$ from $11 x$ .

$\frac{10 x}{2} = 10$

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 x$ .

$\frac{2 (5 x)}{2} = 10$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (5 x)}{2 (1)} = 10$

Cancel the common factor.

$\frac{2 (5 x)}{2 \cdot 1} = 10$

Rewrite the expression.

$\frac{5 x}{1} = 10$

Divide $5 x$ by $1$ .

$5 x = 10$

Step 4

Divide each term in $5 x = 10$ by $5$ and simplify.

Divide each term in $5 x = 10$ by $5$ .

$\frac{5 x}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{10}{5}$

Divide $x$ by $1$ .

$x = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x = 2$

Solve for x 5x+1/2x=1/2x+10

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