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

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

Step 3

Multiply both sides of the equation by $4$ .

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

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 $4$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

Multiply $4$ by $3$ .

$k = 12 + 4 (- \frac{j}{2})$

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 $- \frac{j}{2}$ into the numerator.

$k = 12 + 4 \frac{- j}{2}$

Step 4.2.1.3.2

Factor $2$ out of $4$ .

$k = 12 + 2 (2) \frac{- j}{2}$

Step 4.2.1.3.3

Cancel the common factor.

$k = 12 + 2 \cdot 2 \frac{- j}{2}$

Step 4.2.1.3.4

Rewrite the expression.

$k = 12 + 2 (- j)$

Step 4.2.1.4

Multiply $- 1$ by $2$ .

$k = 12 - 2 j$

Step 5

Reorder $12$ and $- 2 j$ .

$k = - 2 j + 12$

Step 6

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

$f (j) = - 2 j + 12$