Solve for n (n-7)/8+(n+7)/9=5/36

$\frac{n - 7}{8} + \frac{n + 7}{9} = \frac{5}{36}$

Step 1

Simplify $\frac{n - 7}{8} + \frac{n + 7}{9}$ .

To write $\frac{n - 7}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{n - 7}{8} \cdot \frac{9}{9} + \frac{n + 7}{9} = \frac{5}{36}$

To write $\frac{n + 7}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{n - 7}{8} \cdot \frac{9}{9} + \frac{n + 7}{9} \cdot \frac{8}{8} = \frac{5}{36}$

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{n - 7}{8}$ by $\frac{9}{9}$ .

$\frac{(n - 7) \cdot 9}{8 \cdot 9} + \frac{n + 7}{9} \cdot \frac{8}{8} = \frac{5}{36}$

Multiply $8$ by $9$ .

$\frac{(n - 7) \cdot 9}{72} + \frac{n + 7}{9} \cdot \frac{8}{8} = \frac{5}{36}$

Multiply $\frac{n + 7}{9}$ by $\frac{8}{8}$ .

$\frac{(n - 7) \cdot 9}{72} + \frac{(n + 7) \cdot 8}{9 \cdot 8} = \frac{5}{36}$

Multiply $9$ by $8$ .

$\frac{(n - 7) \cdot 9}{72} + \frac{(n + 7) \cdot 8}{72} = \frac{5}{36}$

Combine the numerators over the common denominator.

$\frac{(n - 7) \cdot 9 + (n + 7) \cdot 8}{72} = \frac{5}{36}$

Simplify the numerator.

Apply the distributive property.

$\frac{n \cdot 9 - 7 \cdot 9 + (n + 7) \cdot 8}{72} = \frac{5}{36}$

Move $9$ to the left of $n$ .

$\frac{9 \cdot n - 7 \cdot 9 + (n + 7) \cdot 8}{72} = \frac{5}{36}$

Multiply $- 7$ by $9$ .

$\frac{9 \cdot n - 63 + (n + 7) \cdot 8}{72} = \frac{5}{36}$

Apply the distributive property.

$\frac{9 n - 63 + n \cdot 8 + 7 \cdot 8}{72} = \frac{5}{36}$

Move $8$ to the left of $n$ .

$\frac{9 n - 63 + 8 \cdot n + 7 \cdot 8}{72} = \frac{5}{36}$

Multiply $7$ by $8$ .

$\frac{9 n - 63 + 8 \cdot n + 56}{72} = \frac{5}{36}$

Add $9 n$ and $8 n$ .

$\frac{17 n - 63 + 56}{72} = \frac{5}{36}$

Add $- 63$ and $56$ .

$\frac{17 n - 7}{72} = \frac{5}{36}$

Step 2

Multiply both sides by $72$ .

$\frac{17 n - 7}{72} \cdot 72 = \frac{5}{36} \cdot 72$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $72$ .

Cancel the common factor.

$\frac{17 n - 7}{72} \cdot 72 = \frac{5}{36} \cdot 72$

Rewrite the expression.

$17 n - 7 = \frac{5}{36} \cdot 72$

Simplify the right side.

Simplify $\frac{5}{36} \cdot 72$ .

Cancel the common factor of $36$ .

Factor $36$ out of $72$ .

$17 n - 7 = \frac{5}{36} \cdot (36 (2))$

Cancel the common factor.

$17 n - 7 = \frac{5}{36} \cdot (36 \cdot 2)$

Rewrite the expression.

$17 n - 7 = 5 \cdot 2$

Multiply $5$ by $2$ .

$17 n - 7 = 10$

Step 4

Solve for $n$ .

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

Add $7$ to both sides of the equation.

$17 n = 10 + 7$

Add $10$ and $7$ .

$17 n = 17$

Divide each term in $17 n = 17$ by $17$ and simplify.

Divide each term in $17 n = 17$ by $17$ .

$\frac{17 n}{17} = \frac{17}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 n}{17} = \frac{17}{17}$

Divide $n$ by $1$ .

$n = \frac{17}{17}$

Simplify the right side.

Divide $17$ by $17$ .

$n = 1$

Solve for n (n-7)/8+(n+7)/9=5/36

Related Questions

Support LCMGCF.com by disabling your adblocker.