Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{x}{2} = 3 - \frac{1}{2}$

Step 1.2

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

$\frac{x}{2} = 3 \cdot \frac{2}{2} - \frac{1}{2}$

Step 1.3

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

$\frac{x}{2} = \frac{3 \cdot 2}{2} - \frac{1}{2}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x}{2} = \frac{3 \cdot 2 - 1}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3$ by $2$ .

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

Step 1.5.2

Subtract $1$ from $6$ .

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

Step 2

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

$x = 5$