Pre-Algebra Examples

$\frac{- 3 j - (- 4)}{- 6} = 12$

Step 1

Multiply both sides by $- 6$ .

$\frac{- 3 j - (- 4)}{- 6} \cdot - 6 = 12 \cdot - 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{- 3 j - (- 4)}{- 6} \cdot - 6$ .

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Step 2.1.1.1

Multiply $- 1$ by $- 4$ .

$\frac{- 3 j + 4}{- 6} \cdot - 6 = 12 \cdot - 6$

Step 2.1.1.2

Cancel the common factor of $6$ .

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Step 2.1.1.2.1

Factor $6$ out of $- 6$ .

$\frac{- 3 j + 4}{6 (- 1)} \cdot - 6 = 12 \cdot - 6$

Step 2.1.1.2.2

Factor $6$ out of $- 6$ .

$\frac{- 3 j + 4}{6 \cdot - 1} \cdot (6 \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.2.3

Cancel the common factor.

$\frac{- 3 j + 4}{6 \cdot - 1} \cdot (6 \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.2.4

Rewrite the expression.

$\frac{- 3 j + 4}{- 1} \cdot - 1 = 12 \cdot - 6$

Step 2.1.1.3

Combine $\frac{- 3 j + 4}{- 1}$ and $- 1$ .

$\frac{(- 3 j + 4) \cdot - 1}{- 1} = 12 \cdot - 6$

Step 2.1.1.4

Simplify the expression.

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Step 2.1.1.4.1

Move the negative one from the denominator of $\frac{(- 3 j + 4) \cdot - 1}{- 1}$ .

$- 1 \cdot ((- 3 j + 4) \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.4.2

Rewrite $- 1 \cdot ((- 3 j + 4) \cdot - 1)$ as $- ((- 3 j + 4) \cdot - 1)$ .

$- ((- 3 j + 4) \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.5

Apply the distributive property.

$- (- 3 j \cdot - 1 + 4 \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.6

Multiply.

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Step 2.1.1.6.1

Multiply $- 1$ by $- 3$ .

$- (3 j + 4 \cdot - 1) = 12 \cdot - 6$

Step 2.1.1.6.2

Multiply $4$ by $- 1$ .

$- (3 j - 4) = 12 \cdot - 6$

Step 2.1.1.7

Apply the distributive property.

$- (3 j) - - 4 = 12 \cdot - 6$

Step 2.1.1.8

Multiply.

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Step 2.1.1.8.1

Multiply $3$ by $- 1$ .

$- 3 j - - 4 = 12 \cdot - 6$

Step 2.1.1.8.2

Multiply $- 1$ by $- 4$ .

$- 3 j + 4 = 12 \cdot - 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $12$ by $- 6$ .

$- 3 j + 4 = - 72$

Step 3

Solve for $j$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4$ from both sides of the equation.

$- 3 j = - 72 - 4$

Step 3.1.2

Subtract $4$ from $- 72$ .

$- 3 j = - 76$

Step 3.2

Divide each term in $- 3 j = - 76$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 j = - 76$ by $- 3$ .

$\frac{- 3 j}{- 3} = \frac{- 76}{- 3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 j}{- 3} = \frac{- 76}{- 3}$

Step 3.2.2.1.2

Divide $j$ by $1$ .

$j = \frac{- 76}{- 3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Dividing two negative values results in a positive value.

$j = \frac{76}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$j = \frac{76}{3}$

Decimal Form:

$j = 25.\overline{3}$

Mixed Number Form:

$j = 25 \frac{1}{3}$