Algebra Examples

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

Step 1

Simplify $\frac{x + 1}{2} - \frac{x}{6}$ .

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Step 1.1

To write $\frac{x + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 1}{2} \cdot \frac{3}{3} - \frac{x}{6} = \frac{1}{2}$

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 $\frac{x + 1}{2}$ by $\frac{3}{3}$ .

$\frac{(x + 1) \cdot 3}{2 \cdot 3} - \frac{x}{6} = \frac{1}{2}$

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{(x + 1) \cdot 3}{6} - \frac{x}{6} = \frac{1}{2}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{(x + 1) \cdot 3 - x}{6} = \frac{1}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Apply the distributive property.

$\frac{x \cdot 3 + 1 \cdot 3 - x}{6} = \frac{1}{2}$

Step 1.4.2

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 1 \cdot 3 - x}{6} = \frac{1}{2}$

Step 1.4.3

Multiply $3$ by $1$ .

$\frac{3 \cdot x + 3 - x}{6} = \frac{1}{2}$

Step 1.4.4

Subtract $x$ from $3 x$ .

$\frac{2 x + 3}{6} = \frac{1}{2}$

Step 2

Multiply both sides by $6$ .

$\frac{2 x + 3}{6} \cdot 6 = \frac{1}{2} \cdot 6$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{2 x + 3}{6} \cdot 6 = \frac{1}{2} \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$2 x + 3 = \frac{1}{2} \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $6$ .

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$2 x + 3 = 3$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$2 x = 3 - 3$

Step 4.1.2

Subtract $3$ from $3$ .

$2 x = 0$

Step 4.2

Divide each term in $2 x = 0$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0$ by $2$ .

$x = 0$