Algebra Examples

$\frac{1}{2} n + 7 = \frac{n + 14}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{1}{2} n + 7) \cdot 2 = \frac{n + 14}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{1}{2} n + 7) \cdot 2$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $n$ .

$(\frac{n}{2} + 7) \cdot 2 = \frac{n + 14}{2} \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$\frac{n}{2} \cdot 2 + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{n}{2} \cdot 2 + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Step 2.1.1.3.2

Rewrite the expression.

$n + 7 \cdot 2 = \frac{n + 14}{2} \cdot 2$

Step 2.1.1.4

Multiply $7$ by $2$ .

$n + 14 = \frac{n + 14}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$n + 14 = \frac{n + 14}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$n + 14 = n + 14$

Step 3

Solve for $n$ .

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Step 3.1

Move all terms containing $n$ to the left side of the equation.

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Step 3.1.1

Subtract $n$ from both sides of the equation.

$n + 14 - n = 14$

Step 3.1.2

Combine the opposite terms in $n + 14 - n$ .

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Step 3.1.2.1

Subtract $n$ from $n$ .

$0 + 14 = 14$

Step 3.1.2.2

Add $0$ and $14$ .

$14 = 14$

Step 3.2

Since $14 = 14$ , the equation will always be true for any value of $n$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$