Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Combine $\frac{1}{4}$ and $k$ .

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

Step 2

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

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

Step 3

Multiply both sides of the equation by $2$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $2 (3 - \frac{k}{4})$ .

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Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

Multiply $2$ by $3$ .

$j = 6 + 2 (- \frac{k}{4})$

Step 4.2.1.3

Cancel the common factor of $2$ .

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Step 4.2.1.3.1

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

$j = 6 + 2 \frac{- k}{4}$

Step 4.2.1.3.2

Factor $2$ out of $4$ .

$j = 6 + 2 \frac{- k}{2 (2)}$

Step 4.2.1.3.3

Cancel the common factor.

$j = 6 + 2 \frac{- k}{2 \cdot 2}$

Step 4.2.1.3.4

Rewrite the expression.

$j = 6 + \frac{- k}{2}$

Step 4.2.1.4

Move the negative in front of the fraction.

$j = 6 - \frac{k}{2}$

Step 5

Reorder $6$ and $- \frac{k}{2}$ .

$j = - \frac{k}{2} + 6$

Step 6

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

$f (k) = - \frac{k}{2} + 6$