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

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

Step 1

Simplify $3 (\frac{1}{4} k + 1)$ .

Rewrite.

$0 + 0 + 3 (\frac{1}{4} k + 1) = k - 4$

Simplify by adding zeros.

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

Combine $\frac{1}{4}$ and $k$ .

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

Apply the distributive property.

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

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

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

Multiply $3$ by $1$ .

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

Step 2

Move all terms containing $k$ to the left side of the equation.

Subtract $k$ from both sides of the equation.

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

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

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

Combine $- k$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $k$ out of $3 k - k \cdot 4$ .

Factor $k$ out of $3 k$ .

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

Factor $k$ out of $- k \cdot 4$ .

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

Factor $k$ out of $k \cdot 3 + k (- 1 \cdot 4)$ .

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

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $3$ .

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

Move $- 1$ to the left of $k$ .

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

Move the negative in front of the fraction.

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

Step 3

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $- 4$ .

$- \frac{k}{4} = - 7$

Step 4

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{k}{4}) = - 4 \cdot - 7$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{k}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{k}{4}$ into the numerator.

$- 4 \frac{- k}{4} = - 4 \cdot - 7$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- k}{4} = - 4 \cdot - 7$

Cancel the common factor.

$4 \cdot - 1 \frac{- k}{4} = - 4 \cdot - 7$

Rewrite the expression.

$- - k = - 4 \cdot - 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k = - 4 \cdot - 7$

Multiply $k$ by $1$ .

$k = - 4 \cdot - 7$

Simplify the right side.

Multiply $- 4$ by $- 7$ .

$k = 28$

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

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