Algebra Examples

$\frac{x}{3} + \frac{x}{6} = \frac{7}{2}$

Step 1

Simplify $\frac{x}{3} + \frac{x}{6}$ .

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Step 1.1

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

$\frac{x}{3} \cdot \frac{2}{2} + \frac{x}{6} = \frac{7}{2}$

Step 1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{3 \cdot 2} + \frac{x}{6} = \frac{7}{2}$

Step 1.2.2

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} + \frac{x}{6} = \frac{7}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{6} = \frac{7}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + x}{6} = \frac{7}{2}$

Step 1.4.2

Add $2 x$ and $x$ .

$\frac{3 x}{6} = \frac{7}{2}$

Step 1.5

Cancel the common factor of $3$ and $6$ .

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Step 1.5.1

Factor $3$ out of $3 x$ .

$\frac{3 (x)}{6} = \frac{7}{2}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $6$ .

$\frac{3 x}{3 \cdot 2} = \frac{7}{2}$

Step 1.5.2.2

Cancel the common factor.

$\frac{3 x}{3 \cdot 2} = \frac{7}{2}$

Step 1.5.2.3

Rewrite the expression.

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

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = 7$