Algebra Examples

$(7 j + \frac{1}{8} q + 3) - (\frac{5}{8} q - 11 + 2 j)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{8}$ and $q$ .

$7 j + \frac{q}{8} + 3 - (\frac{5}{8} q - 11 + 2 j)$

Step 1.2

Combine $\frac{5}{8}$ and $q$ .

$7 j + \frac{q}{8} + 3 - (\frac{5 q}{8} - 11 + 2 j)$

Step 1.3

Apply the distributive property.

$7 j + \frac{q}{8} + 3 - \frac{5 q}{8} - - 11 - (2 j)$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $- 1$ by $- 11$ .

$7 j + \frac{q}{8} + 3 - \frac{5 q}{8} + 11 - (2 j)$

Step 1.4.2

Multiply $2$ by $- 1$ .

$7 j + \frac{q}{8} + 3 - \frac{5 q}{8} + 11 - 2 j$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$7 j + 3 + 11 - 2 j + \frac{q - 5 q}{8}$

Step 2.2

Subtract $5 q$ from $q$ .

$7 j + 3 + 11 - 2 j + \frac{- 4 q}{8}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $- 4$ and $8$ .

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Step 3.1.1

Factor $4$ out of $- 4 q$ .

$7 j + 3 + 11 - 2 j + \frac{4 (- q)}{8}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $8$ .

$7 j + 3 + 11 - 2 j + \frac{4 (- q)}{4 (2)}$

Step 3.1.2.2

Cancel the common factor.

$7 j + 3 + 11 - 2 j + \frac{4 (- q)}{4 \cdot 2}$

Step 3.1.2.3

Rewrite the expression.

$7 j + 3 + 11 - 2 j + \frac{- q}{2}$

Step 3.2

Move the negative in front of the fraction.

$7 j + 3 + 11 - 2 j - \frac{q}{2}$

Step 4

Simplify by adding terms.

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Step 4.1

Subtract $2 j$ from $7 j$ .

$5 j + 3 + 11 - \frac{q}{2}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Add $3$ and $11$ .

$5 j + 14 - \frac{q}{2}$

Step 4.2.2

Move $14$ .

$5 j - \frac{q}{2} + 14$