Algebra Examples

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

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.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Factor $3$ out of $3 k$ .

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

Step 2.1.3.2

Cancel the common factor.

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

Step 2.1.3.3

Rewrite the expression.

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

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Factor $3$ out of $- 3$ .

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

Step 2.1.4.2

Cancel the common factor.

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

Step 2.1.4.3

Rewrite the expression.

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

Step 2.2

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

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

Step 2.3

Simplify terms.

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Step 2.3.1

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

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

Step 2.3.2

Combine the numerators over the common denominator.

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

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $k$ out of $k + 2 k \cdot 2$ .

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Step 2.4.1.1.1

Raise $k$ to the power of $1$ .

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

Step 2.4.1.1.2

Factor $k$ out of $k^{1}$ .

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

Step 2.4.1.1.3

Factor $k$ out of $2 k \cdot 2$ .

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

Step 2.4.1.1.4

Factor $k$ out of $k \cdot 1 + k (2 \cdot 2)$ .

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

Step 2.4.1.2

Multiply $2$ by $2$ .

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

Step 2.4.1.3

Add $1$ and $4$ .

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

Step 2.4.2

Move $5$ to the left of $k$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Subtract $\frac{3 k}{5}$ from both sides of the equation.

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

Step 4.2

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

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

Step 4.3

To write $- \frac{3 k}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.4

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

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Step 4.4.1

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

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

Step 4.4.2

Multiply $2$ by $5$ .

$\frac{5 k \cdot 5}{10} - \frac{3 k}{5} \cdot \frac{2}{2} - 1 = 0$

Step 4.4.3

Multiply $\frac{3 k}{5}$ by $\frac{2}{2}$ .

$\frac{5 k \cdot 5}{10} - \frac{3 k \cdot 2}{5 \cdot 2} - 1 = 0$

Step 4.4.4

Multiply $5$ by $2$ .

$\frac{5 k \cdot 5}{10} - \frac{3 k \cdot 2}{10} - 1 = 0$

Step 4.5

Combine the numerators over the common denominator.

$\frac{5 k \cdot 5 - 3 k \cdot 2}{10} - 1 = 0$

Step 4.6

Simplify each term.

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Step 4.6.1

Simplify the numerator.

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Step 4.6.1.1

Factor $k$ out of $5 k \cdot 5 - 3 k \cdot 2$ .

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Step 4.6.1.1.1

Factor $k$ out of $5 k \cdot 5$ .

$\frac{k (5 \cdot 5) - 3 k \cdot 2}{10} - 1 = 0$

Step 4.6.1.1.2

Factor $k$ out of $- 3 k \cdot 2$ .

$\frac{k (5 \cdot 5) + k (- 3 \cdot 2)}{10} - 1 = 0$

Step 4.6.1.1.3

Factor $k$ out of $k (5 \cdot 5) + k (- 3 \cdot 2)$ .

$\frac{k (5 \cdot 5 - 3 \cdot 2)}{10} - 1 = 0$

Step 4.6.1.2

Multiply $5$ by $5$ .

$\frac{k (25 - 3 \cdot 2)}{10} - 1 = 0$

Step 4.6.1.3

Multiply $- 3$ by $2$ .

$\frac{k (25 - 6)}{10} - 1 = 0$

Step 4.6.1.4

Subtract $6$ from $25$ .

$\frac{k \cdot 19}{10} - 1 = 0$

Step 4.6.2

Move $19$ to the left of $k$ .

$\frac{19 k}{10} - 1 = 0$

Step 5

Add $1$ to both sides of the equation.

$\frac{19 k}{10} = 1$

Step 6

Multiply both sides of the equation by $\frac{10}{19}$ .

$\frac{10}{19} \cdot \frac{19 k}{10} = \frac{10}{19} \cdot 1$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $\frac{10}{19} \cdot \frac{19 k}{10}$ .

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Step 7.1.1.1

Cancel the common factor of $10$ .

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Step 7.1.1.1.1

Cancel the common factor.

$\frac{10}{19} \cdot \frac{19 k}{10} = \frac{10}{19} \cdot 1$

Step 7.1.1.1.2

Rewrite the expression.

$\frac{1}{19} (19 k) = \frac{10}{19} \cdot 1$

Step 7.1.1.2

Cancel the common factor of $19$ .

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Step 7.1.1.2.1

Factor $19$ out of $19 k$ .

$\frac{1}{19} (19 (k)) = \frac{10}{19} \cdot 1$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{1}{19} (19 k) = \frac{10}{19} \cdot 1$

Step 7.1.1.2.3

Rewrite the expression.

$k = \frac{10}{19} \cdot 1$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $\frac{10}{19}$ by $1$ .

$k = \frac{10}{19}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$k = \frac{10}{19}$

Decimal Form:

$k = 0.52631578 \dots$