Algebra Examples

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

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.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Cancel the common factor.

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

Step 2.1.3.2

Rewrite the expression.

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

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{2 k}{3}$ into the numerator.

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

Step 2.1.4.2

Cancel the common factor.

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

Step 2.1.4.3

Rewrite the expression.

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

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

Factor $2$ out of $- 2 k$ .

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

Step 2.1.5.2

Cancel the common factor.

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

Step 2.1.5.3

Rewrite the expression.

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

Step 2.2

Subtract $k$ from $- 2 k$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Subtract $\frac{3 k}{4}$ from both sides of the equation.

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

Step 4.2

To write $- 3 k$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify each term.

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Step 4.5.1

Simplify the numerator.

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Step 4.5.1.1

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

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Step 4.5.1.1.1

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

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

Step 4.5.1.1.2

Factor $3 k$ out of $- 3 k$ .

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

Step 4.5.1.1.3

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

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

Step 4.5.1.2

Multiply $- 1$ by $4$ .

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

Step 4.5.1.3

Subtract $1$ from $- 4$ .

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

Step 4.5.1.4

Multiply $- 5$ by $3$ .

$\frac{- 15 k}{4} + 3 = - 3$

Step 4.5.2

Move the negative in front of the fraction.

$- \frac{15 k}{4} + 3 = - 3$

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.

$- \frac{15 k}{4} = - 3 - 3$

Step 5.2

Subtract $3$ from $- 3$ .

$- \frac{15 k}{4} = - 6$

Step 6

Multiply both sides of the equation by $- \frac{4}{15}$ .

$- \frac{4}{15} (- \frac{15 k}{4}) = - \frac{4}{15} \cdot - 6$

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 $- \frac{4}{15} (- \frac{15 k}{4})$ .

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Step 7.1.1.1

Cancel the common factor of $4$ .

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Step 7.1.1.1.1

Move the leading negative in $- \frac{4}{15}$ into the numerator.

$\frac{- 4}{15} (- \frac{15 k}{4}) = - \frac{4}{15} \cdot - 6$

Step 7.1.1.1.2

Move the leading negative in $- \frac{15 k}{4}$ into the numerator.

$\frac{- 4}{15} \cdot \frac{- 15 k}{4} = - \frac{4}{15} \cdot - 6$

Step 7.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{15} \cdot \frac{- 15 k}{4} = - \frac{4}{15} \cdot - 6$

Step 7.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{15} \cdot \frac{- 15 k}{4} = - \frac{4}{15} \cdot - 6$

Step 7.1.1.1.5

Rewrite the expression.

$\frac{- 1}{15} (- 15 k) = - \frac{4}{15} \cdot - 6$

Step 7.1.1.2

Cancel the common factor of $15$ .

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Step 7.1.1.2.1

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

$\frac{- 1}{15} (15 (- k)) = - \frac{4}{15} \cdot - 6$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{- 1}{15} (15 (- k)) = - \frac{4}{15} \cdot - 6$

Step 7.1.1.2.3

Rewrite the expression.

$- - k = - \frac{4}{15} \cdot - 6$

Step 7.1.1.3

Multiply.

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Step 7.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 k = - \frac{4}{15} \cdot - 6$

Step 7.1.1.3.2

Multiply $k$ by $1$ .

$k = - \frac{4}{15} \cdot - 6$

Step 7.2

Simplify the right side.

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Step 7.2.1

Simplify $- \frac{4}{15} \cdot - 6$ .

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Step 7.2.1.1

Cancel the common factor of $3$ .

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Step 7.2.1.1.1

Move the leading negative in $- \frac{4}{15}$ into the numerator.

$k = \frac{- 4}{15} \cdot - 6$

Step 7.2.1.1.2

Factor $3$ out of $15$ .

$k = \frac{- 4}{3 (5)} \cdot - 6$

Step 7.2.1.1.3

Factor $3$ out of $- 6$ .

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

Step 7.2.1.1.4

Cancel the common factor.

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

Step 7.2.1.1.5

Rewrite the expression.

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

Step 7.2.1.2

Combine $\frac{- 4}{5}$ and $- 2$ .

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

Step 7.2.1.3

Multiply $- 4$ by $- 2$ .

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$k = 1.6$

Mixed Number Form:

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