Solve for k 4/5k=-2k+1/2+3/10k-2

$\frac{4}{5} k = - 2 k + \frac{1}{2} + \frac{3}{10} k - 2$

Step 1

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 2 k + \frac{1}{2} + \frac{3}{10} k - 2 = \frac{4}{5} k$

Step 2

Simplify $- 2 k + \frac{1}{2} + \frac{3}{10} k - 2$ .

Combine $\frac{3}{10}$ and $k$ .

$- 2 k + \frac{1}{2} + \frac{3 k}{10} - 2 = \frac{4}{5} k$

To write $- 2 k$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- 2 k \cdot \frac{10}{10} + \frac{3 k}{10} + \frac{1}{2} - 2 = \frac{4}{5} k$

Combine $- 2 k$ and $\frac{10}{10}$ .

$\frac{- 2 k \cdot 10}{10} + \frac{3 k}{10} + \frac{1}{2} - 2 = \frac{4}{5} k$

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{1}{2} - 2 = \frac{4}{5} k$

Find the common denominator.

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{1}{2} \cdot \frac{5}{5} - 2 = \frac{4}{5} k$

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{5}{2 \cdot 5} - 2 = \frac{4}{5} k$

Write $- 2$ as a fraction with denominator $1$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{5}{2 \cdot 5} + \frac{- 2}{1} = \frac{4}{5} k$

Multiply $\frac{- 2}{1}$ by $\frac{10}{10}$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{5}{2 \cdot 5} + \frac{- 2}{1} \cdot \frac{10}{10} = \frac{4}{5} k$

Multiply $\frac{- 2}{1}$ by $\frac{10}{10}$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{5}{2 \cdot 5} + \frac{- 2 \cdot 10}{10} = \frac{4}{5} k$

Multiply $2$ by $5$ .

$\frac{- 2 k \cdot 10 + 3 k}{10} + \frac{5}{10} + \frac{- 2 \cdot 10}{10} = \frac{4}{5} k$

Combine the numerators over the common denominator.

$\frac{- 2 k \cdot 10 + 3 k + 5 - 2 \cdot 10}{10} = \frac{4}{5} k$

Simplify each term.

Multiply $10$ by $- 2$ .

$\frac{- 20 k + 3 k + 5 - 2 \cdot 10}{10} = \frac{4}{5} k$

Multiply $- 2$ by $10$ .

$\frac{- 20 k + 3 k + 5 - 20}{10} = \frac{4}{5} k$

Simplify terms.

Add $- 20 k$ and $3 k$ .

$\frac{- 17 k + 5 - 20}{10} = \frac{4}{5} k$

Subtract $20$ from $5$ .

$\frac{- 17 k - 15}{10} = \frac{4}{5} k$

Factor $- 1$ out of $- 17 k$ .

$\frac{- (17 k) - 15}{10} = \frac{4}{5} k$

Rewrite $- 15$ as $- 1 (15)$ .

$\frac{- (17 k) - 1 (15)}{10} = \frac{4}{5} k$

Factor $- 1$ out of $- (17 k) - 1 (15)$ .

$\frac{- (17 k + 15)}{10} = \frac{4}{5} k$

Simplify the expression.

Rewrite $- (17 k + 15)$ as $- 1 (17 k + 15)$ .

$\frac{- 1 (17 k + 15)}{10} = \frac{4}{5} k$

Move the negative in front of the fraction.

$- \frac{17 k + 15}{10} = \frac{4}{5} k$

Step 3

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

$- \frac{17 k + 15}{10} = \frac{4 k}{5}$

Step 4

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

Subtract $\frac{4 k}{5}$ from both sides of the equation.

$- \frac{17 k + 15}{10} - \frac{4 k}{5} = 0$

To write $- \frac{4 k}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{17 k + 15}{10} - \frac{4 k}{5} \cdot \frac{2}{2} = 0$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 k}{5}$ by $\frac{2}{2}$ .

$- \frac{17 k + 15}{10} - \frac{4 k \cdot 2}{5 \cdot 2} = 0$

Multiply $5$ by $2$ .

$- \frac{17 k + 15}{10} - \frac{4 k \cdot 2}{10} = 0$

Combine the numerators over the common denominator.

$\frac{- (17 k + 15) - 4 k \cdot 2}{10} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{- (17 k) - 1 \cdot 15 - 4 k \cdot 2}{10} = 0$

Multiply $17$ by $- 1$ .

$\frac{- 17 k - 1 \cdot 15 - 4 k \cdot 2}{10} = 0$

Multiply $- 1$ by $15$ .

$\frac{- 17 k - 15 - 4 k \cdot 2}{10} = 0$

Multiply $2$ by $- 4$ .

$\frac{- 17 k - 15 - 8 k}{10} = 0$

Subtract $8 k$ from $- 17 k$ .

$\frac{- 25 k - 15}{10} = 0$

Factor $5$ out of $- 25 k - 15$ .

Factor $5$ out of $- 25 k$ .

$\frac{5 (- 5 k) - 15}{10} = 0$

Factor $5$ out of $- 15$ .

$\frac{5 (- 5 k) + 5 (- 3)}{10} = 0$

Factor $5$ out of $5 (- 5 k) + 5 (- 3)$ .

$\frac{5 (- 5 k - 3)}{10} = 0$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (- 5 k - 3)}{5 \cdot 2} = 0$

Cancel the common factor.

$\frac{5 (- 5 k - 3)}{5 \cdot 2} = 0$

Rewrite the expression.

$\frac{- 5 k - 3}{2} = 0$

Factor $- 1$ out of $- 5 k$ .

$\frac{- (5 k) - 3}{2} = 0$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (5 k) - 1 (3)}{2} = 0$

Factor $- 1$ out of $- (5 k) - 1 (3)$ .

$\frac{- (5 k + 3)}{2} = 0$

Rewrite $- (5 k + 3)$ as $- 1 (5 k + 3)$ .

$\frac{- 1 (5 k + 3)}{2} = 0$

Move the negative in front of the fraction.

$- \frac{5 k + 3}{2} = 0$

Step 5

Set the numerator equal to zero.

$5 k + 3 = 0$

Step 6

Solve the equation for $k$ .

Subtract $3$ from both sides of the equation.

$5 k = - 3$

Divide each term in $5 k = - 3$ by $5$ and simplify.

Divide each term in $5 k = - 3$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$k = - 0.6$

Solve for k 4/5k=-2k+1/2+3/10k-2

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