Basic Math Examples

$\frac{k - 3}{7} + \frac{k + 5}{3} = 6$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{k - 3}{7} \cdot \frac{3}{3} + \frac{k + 5}{3} = 6$

Step 1.2

To write $\frac{k + 5}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{k - 3}{7} \cdot \frac{3}{3} + \frac{k + 5}{3} \cdot \frac{7}{7} = 6$

Step 1.3

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{k - 3}{7}$ by $\frac{3}{3}$ .

$\frac{(k - 3) \cdot 3}{7 \cdot 3} + \frac{k + 5}{3} \cdot \frac{7}{7} = 6$

Step 1.3.2

Multiply $7$ by $3$ .

$\frac{(k - 3) \cdot 3}{21} + \frac{k + 5}{3} \cdot \frac{7}{7} = 6$

Step 1.3.3

Multiply $\frac{k + 5}{3}$ by $\frac{7}{7}$ .

$\frac{(k - 3) \cdot 3}{21} + \frac{(k + 5) \cdot 7}{3 \cdot 7} = 6$

Step 1.3.4

Multiply $3$ by $7$ .

$\frac{(k - 3) \cdot 3}{21} + \frac{(k + 5) \cdot 7}{21} = 6$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(k - 3) \cdot 3 + (k + 5) \cdot 7}{21} = 6$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$\frac{k \cdot 3 - 3 \cdot 3 + (k + 5) \cdot 7}{21} = 6$

Step 1.5.2

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

$\frac{3 \cdot k - 3 \cdot 3 + (k + 5) \cdot 7}{21} = 6$

Step 1.5.3

Multiply $- 3$ by $3$ .

$\frac{3 \cdot k - 9 + (k + 5) \cdot 7}{21} = 6$

Step 1.5.4

Apply the distributive property.

$\frac{3 k - 9 + k \cdot 7 + 5 \cdot 7}{21} = 6$

Step 1.5.5

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

$\frac{3 k - 9 + 7 \cdot k + 5 \cdot 7}{21} = 6$

Step 1.5.6

Multiply $5$ by $7$ .

$\frac{3 k - 9 + 7 \cdot k + 35}{21} = 6$

Step 1.5.7

Add $3 k$ and $7 k$ .

$\frac{10 k - 9 + 35}{21} = 6$

Step 1.5.8

Add $- 9$ and $35$ .

$\frac{10 k + 26}{21} = 6$

Step 1.5.9

Factor $2$ out of $10 k + 26$ .

Tap for more steps...

Step 1.5.9.1

Factor $2$ out of $10 k$ .

$\frac{2 (5 k) + 26}{21} = 6$

Step 1.5.9.2

Factor $2$ out of $26$ .

$\frac{2 (5 k) + 2 (13)}{21} = 6$

Step 1.5.9.3

Factor $2$ out of $2 (5 k) + 2 (13)$ .

$\frac{2 (5 k + 13)}{21} = 6$

Step 2

Multiply both sides by $21$ .

$\frac{2 (5 k + 13)}{21} \cdot 21 = 6 \cdot 21$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{2 (5 k + 13)}{21} \cdot 21$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $21$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{2 (5 k + 13)}{21} \cdot 21 = 6 \cdot 21$

Step 3.1.1.1.2

Rewrite the expression.

$2 (5 k + 13) = 6 \cdot 21$

Step 3.1.1.2

Apply the distributive property.

$2 (5 k) + 2 \cdot 13 = 6 \cdot 21$

Step 3.1.1.3

Multiply.

Tap for more steps...

Step 3.1.1.3.1

Multiply $5$ by $2$ .

$10 k + 2 \cdot 13 = 6 \cdot 21$

Step 3.1.1.3.2

Multiply $2$ by $13$ .

$10 k + 26 = 6 \cdot 21$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $6$ by $21$ .

$10 k + 26 = 126$

Step 4

Solve for $k$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $26$ from both sides of the equation.

$10 k = 126 - 26$

Step 4.1.2

Subtract $26$ from $126$ .

$10 k = 100$

Step 4.2

Divide each term in $10 k = 100$ by $10$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $10 k = 100$ by $10$ .

$\frac{10 k}{10} = \frac{100}{10}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{10 k}{10} = \frac{100}{10}$

Step 4.2.2.1.2

Divide $k$ by $1$ .

$k = \frac{100}{10}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $100$ by $10$ .

$k = 10$