Algebra Examples

$k (- 5) = 6 x + 100$

Step 1

Rewrite the equation as $6 x + 100 = k (- 5)$ .

$6 x + 100 = k (- 5)$

Step 2

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

$6 x + 100 = - 5 k$

Step 3

Subtract $100$ from both sides of the equation.

$6 x = - 5 k - 100$

Step 4

Divide each term in $6 x = - 5 k - 100$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x = - 5 k - 100$ by $6$ .

$\frac{6 x}{6} = \frac{- 5 k}{6} + \frac{- 100}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 5 k}{6} + \frac{- 100}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5 k}{6} + \frac{- 100}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$x = - \frac{5 k}{6} + \frac{- 100}{6}$

Step 4.3.1.2

Cancel the common factor of $- 100$ and $6$ .

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Step 4.3.1.2.1

Factor $2$ out of $- 100$ .

$x = - \frac{5 k}{6} + \frac{2 (- 50)}{6}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $2$ out of $6$ .

$x = - \frac{5 k}{6} + \frac{2 \cdot - 50}{2 \cdot 3}$

Step 4.3.1.2.2.2

Cancel the common factor.

$x = - \frac{5 k}{6} + \frac{2 \cdot - 50}{2 \cdot 3}$

Step 4.3.1.2.2.3

Rewrite the expression.

$x = - \frac{5 k}{6} + \frac{- 50}{3}$

Step 4.3.1.3

Move the negative in front of the fraction.

$x = - \frac{5 k}{6} - \frac{50}{3}$

Step 5

To rewrite as a function of $k$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $k$ is on the other side.

$f (k) = - \frac{5 k}{6} - \frac{50}{3}$