Solve for k 5/4k-3/4+1/2k=-1/4k-1/2

$\frac{5}{4} k - \frac{3}{4} + \frac{1}{2} k = - \frac{1}{4} k - \frac{1}{2}$

Simplify $\frac{5}{4} k - \frac{3}{4} + \frac{1}{2} k$ .

Simplify each term.

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

$\frac{5 k}{4} - \frac{3}{4} + \frac{1}{2} k = - \frac{1}{4} k - \frac{1}{2}$

Combine $\frac{1}{2}$ and $k$ .

$\frac{5 k}{4} - \frac{3}{4} + \frac{k}{2} = - \frac{1}{4} k - \frac{1}{2}$

To write $\frac{k}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 k}{4} + \frac{k}{2} \cdot \frac{2}{2} - \frac{3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{k}{2}$ by $\frac{2}{2}$ .

$\frac{5 k}{4} + \frac{k \cdot 2}{2 \cdot 2} - \frac{3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Multiply $2$ by $2$ .

$\frac{5 k}{4} + \frac{k \cdot 2}{4} - \frac{3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{5 k + k \cdot 2}{4} - \frac{3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{5 k + k \cdot 2 - 3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Move $2$ to the left of $k$ .

$\frac{5 k + 2 k - 3}{4} = - \frac{1}{4} k - \frac{1}{2}$

Add $5 k$ and $2 k$ .

$\frac{7 k - 3}{4} = - \frac{1}{4} k - \frac{1}{2}$

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

$\frac{7 k - 3}{4} = - \frac{k}{4} - \frac{1}{2}$

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

Add $\frac{k}{4}$ to both sides of the equation.

$\frac{7 k - 3}{4} + \frac{k}{4} = - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{7 k - 3 + k}{4} = - \frac{1}{2}$

Add $7 k$ and $k$ .

$\frac{8 k - 3}{4} = - \frac{1}{2}$

Multiply both sides by $4$ .

$\frac{8 k - 3}{4} \cdot 4 = - \frac{1}{2} \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{8 k - 3}{4} \cdot 4 = - \frac{1}{2} \cdot 4$

Rewrite the expression.

$8 k - 3 = - \frac{1}{2} \cdot 4$

Simplify the right side.

Simplify $- \frac{1}{2} \cdot 4$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$8 k - 3 = \frac{- 1}{2} \cdot 4$

Factor $2$ out of $4$ .

$8 k - 3 = \frac{- 1}{2} \cdot (2 (2))$

Cancel the common factor.

$8 k - 3 = \frac{- 1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$8 k - 3 = - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$8 k - 3 = - 2$

Solve for $k$ .

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

Add $3$ to both sides of the equation.

$8 k = - 2 + 3$

Add $- 2$ and $3$ .

$8 k = 1$

Divide each term in $8 k = 1$ by $8$ and simplify.

Divide each term in $8 k = 1$ by $8$ .

$\frac{8 k}{8} = \frac{1}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 k}{8} = \frac{1}{8}$

Divide $k$ by $1$ .

$k = \frac{1}{8}$

The result can be shown in multiple forms.

Exact Form:

$k = \frac{1}{8}$

Decimal Form:

$k = 0.125$

Solve for k 5/4k-3/4+1/2k=-1/4k-1/2

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