Solve for x 5x+x/2=11

$5 x + \frac{x}{2} = 11$

Step 1

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

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

$5 x \cdot \frac{2}{2} + \frac{x}{2} = 11$

Simplify terms.

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

$\frac{5 x \cdot 2}{2} + \frac{x}{2} = 11$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 + x}{2} = 11$

Simplify the numerator.

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

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

$\frac{x (5 \cdot 2) + x}{2} = 11$

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

$\frac{x (5 \cdot 2) + x^{1}}{2} = 11$

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

$\frac{x (5 \cdot 2) + x \cdot 1}{2} = 11$

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

$\frac{x (5 \cdot 2 + 1)}{2} = 11$

Multiply $5$ by $2$ .

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

Add $10$ and $1$ .

$\frac{x \cdot 11}{2} = 11$

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

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

Step 2

Multiply both sides of the equation by $\frac{2}{11}$ .

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot 11$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{11} \cdot \frac{11 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot 11$

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{2}{11} \cdot 11$

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{2}{11} \cdot 11$

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{2}{11} \cdot 11$

Rewrite the expression.

$x = \frac{2}{11} \cdot 11$

Simplify the right side.

Cancel the common factor of $11$ .

Cancel the common factor.

$x = \frac{2}{11} \cdot 11$

Rewrite the expression.

$x = 2$

Solve for x 5x+x/2=11

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