Solve for k 1/5(k-3)=3/4

$\frac{1}{5} (k - 3) = \frac{3}{4}$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (k - 3)) = 5 (\frac{3}{4})$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $5 (\frac{1}{5} \cdot (k - 3))$ .

Apply the distributive property.

$5 (\frac{1}{5} k + \frac{1}{5} \cdot - 3) = 5 (\frac{3}{4})$

Combine $\frac{1}{5}$ and $k$ .

$5 (\frac{k}{5} + \frac{1}{5} \cdot - 3) = 5 (\frac{3}{4})$

Combine $\frac{1}{5}$ and $- 3$ .

$5 (\frac{k}{5} + \frac{- 3}{5}) = 5 (\frac{3}{4})$

Move the negative in front of the fraction.

$5 (\frac{k}{5} - \frac{3}{5}) = 5 (\frac{3}{4})$

Apply the distributive property.

$5 \frac{k}{5} + 5 (- \frac{3}{5}) = 5 (\frac{3}{4})$

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{k}{5} + 5 (- \frac{3}{5}) = 5 (\frac{3}{4})$

Rewrite the expression.

$k + 5 (- \frac{3}{5}) = 5 (\frac{3}{4})$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$k + 5 (\frac{- 3}{5}) = 5 (\frac{3}{4})$

Cancel the common factor.

$k + 5 (\frac{- 3}{5}) = 5 (\frac{3}{4})$

Rewrite the expression.

$k - 3 = 5 (\frac{3}{4})$

Simplify the right side.

Multiply $5 (\frac{3}{4})$ .

Combine $5$ and $\frac{3}{4}$ .

$k - 3 = \frac{5 \cdot 3}{4}$

Multiply $5$ by $3$ .

$k - 3 = \frac{15}{4}$

Step 3

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

Add $3$ to both sides of the equation.

$k = \frac{15}{4} + 3$

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

$k = \frac{15}{4} + 3 \cdot \frac{4}{4}$

Combine $3$ and $\frac{4}{4}$ .

$k = \frac{15}{4} + \frac{3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$k = \frac{15 + 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$k = \frac{15 + 12}{4}$

Add $15$ and $12$ .

$k = \frac{27}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{27}{4}$

Decimal Form:

$k = 6.75$

Mixed Number Form:

$k = 6 \frac{3}{4}$

Solve for k 1/5(k-3)=3/4

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