Solve for k (k+1)/3-k/5=3

$\frac{k + 1}{3} - \frac{k}{5} = 3$

Step 1

Simplify $\frac{k + 1}{3} - \frac{k}{5}$ .

To write $\frac{k + 1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{k + 1}{3} \cdot \frac{5}{5} - \frac{k}{5} = 3$

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

$\frac{k + 1}{3} \cdot \frac{5}{5} - \frac{k}{5} \cdot \frac{3}{3} = 3$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{k + 1}{3}$ by $\frac{5}{5}$ .

$\frac{(k + 1) \cdot 5}{3 \cdot 5} - \frac{k}{5} \cdot \frac{3}{3} = 3$

Multiply $3$ by $5$ .

$\frac{(k + 1) \cdot 5}{15} - \frac{k}{5} \cdot \frac{3}{3} = 3$

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

$\frac{(k + 1) \cdot 5}{15} - \frac{k \cdot 3}{5 \cdot 3} = 3$

Multiply $5$ by $3$ .

$\frac{(k + 1) \cdot 5}{15} - \frac{k \cdot 3}{15} = 3$

Combine the numerators over the common denominator.

$\frac{(k + 1) \cdot 5 - k \cdot 3}{15} = 3$

Simplify the numerator.

Apply the distributive property.

$\frac{k \cdot 5 + 1 \cdot 5 - k \cdot 3}{15} = 3$

Move $5$ to the left of $k$ .

$\frac{5 \cdot k + 1 \cdot 5 - k \cdot 3}{15} = 3$

Multiply $5$ by $1$ .

$\frac{5 \cdot k + 5 - k \cdot 3}{15} = 3$

Multiply $3$ by $- 1$ .

$\frac{5 k + 5 - 3 k}{15} = 3$

Subtract $3 k$ from $5 k$ .

$\frac{2 k + 5}{15} = 3$

Step 2

Multiply both sides by $15$ .

$\frac{2 k + 5}{15} \cdot 15 = 3 \cdot 15$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{2 k + 5}{15} \cdot 15 = 3 \cdot 15$

Rewrite the expression.

$2 k + 5 = 3 \cdot 15$

Simplify the right side.

Multiply $3$ by $15$ .

$2 k + 5 = 45$

Step 4

Solve for $k$ .

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

Subtract $5$ from both sides of the equation.

$2 k = 45 - 5$

Subtract $5$ from $45$ .

$2 k = 40$

Divide each term in $2 k = 40$ by $2$ and simplify.

Divide each term in $2 k = 40$ by $2$ .

$\frac{2 k}{2} = \frac{40}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{40}{2}$

Divide $k$ by $1$ .

$k = \frac{40}{2}$

Simplify the right side.

Divide $40$ by $2$ .

$k = 20$

Solve for k (k+1)/3-k/5=3

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