Pre-Algebra Examples

$56 = 50 + \frac{n - 40}{4}$

Step 1

Rewrite the equation as $50 + \frac{n - 40}{4} = 56$ .

$50 + \frac{n - 40}{4} = 56$

Step 2

Simplify $50 + \frac{n - 40}{4}$ .

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Step 2.1

To write $50$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$50 \cdot \frac{4}{4} + \frac{n - 40}{4} = 56$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $50$ and $\frac{4}{4}$ .

$\frac{50 \cdot 4}{4} + \frac{n - 40}{4} = 56$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{50 \cdot 4 + n - 40}{4} = 56$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply $50$ by $4$ .

$\frac{200 + n - 40}{4} = 56$

Step 2.3.2

Subtract $40$ from $200$ .

$\frac{n + 160}{4} = 56$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{n + 160}{4} = 4 \cdot 56$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{n + 160}{4} = 4 \cdot 56$

Step 4.1.1.2

Rewrite the expression.

$n + 160 = 4 \cdot 56$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $56$ .

$n + 160 = 224$

Step 5

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

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Step 5.1

Subtract $160$ from both sides of the equation.

$n = 224 - 160$

Step 5.2

Subtract $160$ from $224$ .

$n = 64$