Finite Math Examples

$- 2 (4 (k + 2) - 3 (k + 1)) = 14 + 2 k$

Step 1

Simplify $- 2 (4 (k + 2) - 3 (k + 1))$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (4 (k + 2) - 3 (k + 1)) = 14 + 2 k$

Step 1.2

Simplify by adding zeros.

$- 2 (4 (k + 2) - 3 (k + 1)) = 14 + 2 k$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$- 2 (4 k + 4 \cdot 2 - 3 (k + 1)) = 14 + 2 k$

Step 1.3.2

Multiply $4$ by $2$ .

$- 2 (4 k + 8 - 3 (k + 1)) = 14 + 2 k$

Step 1.3.3

Apply the distributive property.

$- 2 (4 k + 8 - 3 k - 3 \cdot 1) = 14 + 2 k$

Step 1.3.4

Multiply $- 3$ by $1$ .

$- 2 (4 k + 8 - 3 k - 3) = 14 + 2 k$

Step 1.4

Simplify terms.

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Step 1.4.1

Subtract $3 k$ from $4 k$ .

$- 2 (k + 8 - 3) = 14 + 2 k$

Step 1.4.2

Subtract $3$ from $8$ .

$- 2 (k + 5) = 14 + 2 k$

Step 1.4.3

Apply the distributive property.

$- 2 k - 2 \cdot 5 = 14 + 2 k$

Step 1.4.4

Multiply $- 2$ by $5$ .

$- 2 k - 10 = 14 + 2 k$

Step 2

Move all terms containing $k$ to the left side of the equation.

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Step 2.1

Subtract $2 k$ from both sides of the equation.

$- 2 k - 10 - 2 k = 14$

Step 2.2

Subtract $2 k$ from $- 2 k$ .

$- 4 k - 10 = 14$

Step 3

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

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Step 3.1

Add $10$ to both sides of the equation.

$- 4 k = 14 + 10$

Step 3.2

Add $14$ and $10$ .

$- 4 k = 24$

Step 4

Divide each term in $- 4 k = 24$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 k = 24$ by $- 4$ .

$\frac{- 4 k}{- 4} = \frac{24}{- 4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 4 k}{- 4} = \frac{24}{- 4}$

Step 4.2.1.2

Divide $k$ by $1$ .

$k = \frac{24}{- 4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $24$ by $- 4$ .

$k = - 6$