Algebra Examples

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

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.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{3}{2}$ and $k$ .

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

Step 2.1.2

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

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

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

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

Step 2.2.2

Subtract $k$ from $3 k$ .

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

Step 2.2.3

Cancel the common factor of $2$ .

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Step 2.2.3.1

Cancel the common factor.

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

Step 2.2.3.2

Divide $k$ by $1$ .

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

Step 3

Simplify $2 - k - \frac{2}{5}$ .

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Step 3.1

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

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

Step 3.2

Combine $2$ and $\frac{5}{5}$ .

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $2$ by $5$ .

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

Step 3.4.2

Subtract $2$ from $10$ .

$3 + k = - k + \frac{8}{5}$

Step 4

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

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Step 4.1

Add $k$ to both sides of the equation.

$3 + k + k = \frac{8}{5}$

Step 4.2

Add $k$ and $k$ .

$3 + 2 k = \frac{8}{5}$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$2 k = \frac{8}{5} - 3$

Step 5.2

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

$2 k = \frac{8}{5} - 3 \cdot \frac{5}{5}$

Step 5.3

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

$2 k = \frac{8}{5} + \frac{- 3 \cdot 5}{5}$

Step 5.4

Combine the numerators over the common denominator.

$2 k = \frac{8 - 3 \cdot 5}{5}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $- 3$ by $5$ .

$2 k = \frac{8 - 15}{5}$

Step 5.5.2

Subtract $15$ from $8$ .

$2 k = \frac{- 7}{5}$

Step 5.6

Move the negative in front of the fraction.

$2 k = - \frac{7}{5}$

Step 6

Divide each term in $2 k = - \frac{7}{5}$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 k = - \frac{7}{5}$ by $2$ .

$\frac{2 k}{2} = \frac{- \frac{7}{5}}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{- \frac{7}{5}}{2}$

Step 6.2.1.2

Divide $k$ by $1$ .

$k = \frac{- \frac{7}{5}}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$k = - \frac{7}{5} \cdot \frac{1}{2}$

Step 6.3.2

Multiply $- \frac{7}{5} \cdot \frac{1}{2}$ .

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Step 6.3.2.1

Multiply $\frac{1}{2}$ by $\frac{7}{5}$ .

$k = - \frac{7}{2 \cdot 5}$

Step 6.3.2.2

Multiply $2$ by $5$ .

$k = - \frac{7}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{7}{10}$

Decimal Form:

$k = - 0.7$