Basic Math Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

Move $3$ to the left of $k$ .

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

Step 3

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

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Step 3.1

Add $\frac{3 k}{2}$ to both sides of the equation.

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

Step 3.2

To write $\frac{4 k}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

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

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

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{4 k}{3}$ by $\frac{2}{2}$ .

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

Step 3.4.2

Multiply $3$ by $2$ .

$\frac{4 k \cdot 2}{6} + \frac{3 k}{2} \cdot \frac{3}{3} + \frac{2}{5} = - 1$

Step 3.4.3

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

$\frac{4 k \cdot 2}{6} + \frac{3 k \cdot 3}{2 \cdot 3} + \frac{2}{5} = - 1$

Step 3.4.4

Multiply $2$ by $3$ .

$\frac{4 k \cdot 2}{6} + \frac{3 k \cdot 3}{6} + \frac{2}{5} = - 1$

Step 3.5

Combine the numerators over the common denominator.

$\frac{4 k \cdot 2 + 3 k \cdot 3}{6} + \frac{2}{5} = - 1$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $k$ out of $4 k \cdot 2 + 3 k \cdot 3$ .

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Step 3.6.1.1.1

Factor $k$ out of $4 k \cdot 2$ .

$\frac{k (4 \cdot 2) + 3 k \cdot 3}{6} + \frac{2}{5} = - 1$

Step 3.6.1.1.2

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

$\frac{k (4 \cdot 2) + k (3 \cdot 3)}{6} + \frac{2}{5} = - 1$

Step 3.6.1.1.3

Factor $k$ out of $k (4 \cdot 2) + k (3 \cdot 3)$ .

$\frac{k (4 \cdot 2 + 3 \cdot 3)}{6} + \frac{2}{5} = - 1$

Step 3.6.1.2

Multiply $4$ by $2$ .

$\frac{k (8 + 3 \cdot 3)}{6} + \frac{2}{5} = - 1$

Step 3.6.1.3

Multiply $3$ by $3$ .

$\frac{k (8 + 9)}{6} + \frac{2}{5} = - 1$

Step 3.6.1.4

Add $8$ and $9$ .

$\frac{k \cdot 17}{6} + \frac{2}{5} = - 1$

Step 3.6.2

Move $17$ to the left of $k$ .

$\frac{17 k}{6} + \frac{2}{5} = - 1$

Step 4

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

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Step 4.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$\frac{17 k}{6} = - 1 - \frac{2}{5}$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{17 k}{6} = - 1 \cdot \frac{5}{5} - \frac{2}{5}$

Step 4.3

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{17 k}{6} = \frac{- 1 \cdot 5}{5} - \frac{2}{5}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{17 k}{6} = \frac{- 1 \cdot 5 - 2}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $5$ .

$\frac{17 k}{6} = \frac{- 5 - 2}{5}$

Step 4.5.2

Subtract $2$ from $- 5$ .

$\frac{17 k}{6} = \frac{- 7}{5}$

Step 4.6

Move the negative in front of the fraction.

$\frac{17 k}{6} = - \frac{7}{5}$

Step 5

Multiply both sides of the equation by $\frac{6}{17}$ .

$\frac{6}{17} \cdot \frac{17 k}{6} = \frac{6}{17} (- \frac{7}{5})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{6}{17} \cdot \frac{17 k}{6}$ .

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Step 6.1.1.1

Cancel the common factor of $6$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{6}{17} \cdot \frac{17 k}{6} = \frac{6}{17} (- \frac{7}{5})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{17} (17 k) = \frac{6}{17} (- \frac{7}{5})$

Step 6.1.1.2

Cancel the common factor of $17$ .

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Step 6.1.1.2.1

Factor $17$ out of $17 k$ .

$\frac{1}{17} (17 (k)) = \frac{6}{17} (- \frac{7}{5})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{17} (17 k) = \frac{6}{17} (- \frac{7}{5})$

Step 6.1.1.2.3

Rewrite the expression.

$k = \frac{6}{17} (- \frac{7}{5})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{6}{17} (- \frac{7}{5})$ .

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Step 6.2.1.1

Multiply $\frac{6}{17}$ by $\frac{7}{5}$ .

$k = - \frac{6 \cdot 7}{17 \cdot 5}$

Step 6.2.1.2

Multiply $6$ by $7$ .

$k = - \frac{42}{17 \cdot 5}$

Step 6.2.1.3

Multiply $17$ by $5$ .

$k = - \frac{42}{85}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{42}{85}$

Decimal Form:

$k = - 0.49411764 \dots$