Solve for n (n-3)/4+(n+5)/7=5/14

$\frac{n - 3}{4} + \frac{n + 5}{7} = \frac{5}{14}$

Step 1

Simplify $\frac{n - 3}{4} + \frac{n + 5}{7}$ .

To write $\frac{n - 3}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{n - 3}{4} \cdot \frac{7}{7} + \frac{n + 5}{7} = \frac{5}{14}$

To write $\frac{n + 5}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{n - 3}{4} \cdot \frac{7}{7} + \frac{n + 5}{7} \cdot \frac{4}{4} = \frac{5}{14}$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{n - 3}{4}$ by $\frac{7}{7}$ .

$\frac{(n - 3) \cdot 7}{4 \cdot 7} + \frac{n + 5}{7} \cdot \frac{4}{4} = \frac{5}{14}$

Multiply $4$ by $7$ .

$\frac{(n - 3) \cdot 7}{28} + \frac{n + 5}{7} \cdot \frac{4}{4} = \frac{5}{14}$

Multiply $\frac{n + 5}{7}$ by $\frac{4}{4}$ .

$\frac{(n - 3) \cdot 7}{28} + \frac{(n + 5) \cdot 4}{7 \cdot 4} = \frac{5}{14}$

Multiply $7$ by $4$ .

$\frac{(n - 3) \cdot 7}{28} + \frac{(n + 5) \cdot 4}{28} = \frac{5}{14}$

Combine the numerators over the common denominator.

$\frac{(n - 3) \cdot 7 + (n + 5) \cdot 4}{28} = \frac{5}{14}$

Simplify the numerator.

Apply the distributive property.

$\frac{n \cdot 7 - 3 \cdot 7 + (n + 5) \cdot 4}{28} = \frac{5}{14}$

Move $7$ to the left of $n$ .

$\frac{7 \cdot n - 3 \cdot 7 + (n + 5) \cdot 4}{28} = \frac{5}{14}$

Multiply $- 3$ by $7$ .

$\frac{7 \cdot n - 21 + (n + 5) \cdot 4}{28} = \frac{5}{14}$

Apply the distributive property.

$\frac{7 n - 21 + n \cdot 4 + 5 \cdot 4}{28} = \frac{5}{14}$

Move $4$ to the left of $n$ .

$\frac{7 n - 21 + 4 \cdot n + 5 \cdot 4}{28} = \frac{5}{14}$

Multiply $5$ by $4$ .

$\frac{7 n - 21 + 4 \cdot n + 20}{28} = \frac{5}{14}$

Add $7 n$ and $4 n$ .

$\frac{11 n - 21 + 20}{28} = \frac{5}{14}$

Add $- 21$ and $20$ .

$\frac{11 n - 1}{28} = \frac{5}{14}$

Step 2

Multiply both sides by $28$ .

$\frac{11 n - 1}{28} \cdot 28 = \frac{5}{14} \cdot 28$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{11 n - 1}{28} \cdot 28 = \frac{5}{14} \cdot 28$

Rewrite the expression.

$11 n - 1 = \frac{5}{14} \cdot 28$

Simplify the right side.

Simplify $\frac{5}{14} \cdot 28$ .

Cancel the common factor of $14$ .

Factor $14$ out of $28$ .

$11 n - 1 = \frac{5}{14} \cdot (14 (2))$

Cancel the common factor.

$11 n - 1 = \frac{5}{14} \cdot (14 \cdot 2)$

Rewrite the expression.

$11 n - 1 = 5 \cdot 2$

Multiply $5$ by $2$ .

$11 n - 1 = 10$

Step 4

Solve for $n$ .

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

Add $1$ to both sides of the equation.

$11 n = 10 + 1$

Add $10$ and $1$ .

$11 n = 11$

Divide each term in $11 n = 11$ by $11$ and simplify.

Divide each term in $11 n = 11$ by $11$ .

$\frac{11 n}{11} = \frac{11}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 n}{11} = \frac{11}{11}$

Divide $n$ by $1$ .

$n = \frac{11}{11}$

Simplify the right side.

Divide $11$ by $11$ .

$n = 1$

Solve for n (n-3)/4+(n+5)/7=5/14

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