Algebra Examples

$7 \frac{1}{2} = \frac{x + 3}{2}$

Step 1

Simplify the left side.

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Step 1.1

Convert $7 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$7 + \frac{1}{2} = \frac{x + 3}{2}$

Step 1.1.2

Add $7$ and $\frac{1}{2}$ .

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Step 1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \cdot \frac{2}{2} + \frac{1}{2} = \frac{x + 3}{2}$

Step 1.1.2.2

Combine $7$ and $\frac{2}{2}$ .

$\frac{7 \cdot 2}{2} + \frac{1}{2} = \frac{x + 3}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{2} = \frac{x + 3}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $2$ .

$\frac{14 + 1}{2} = \frac{x + 3}{2}$

Step 1.1.2.4.2

Add $14$ and $1$ .

$\frac{15}{2} = \frac{x + 3}{2}$

Step 2

Rewrite the equation as $\frac{x + 3}{2} = \frac{15}{2}$ .

$\frac{x + 3}{2} = \frac{15}{2}$

Step 3

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

$x + 3 = 15$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

$x = 15 - 3$

Step 4.2

Subtract $3$ from $15$ .

$x = 12$