Basic Math Examples

$3 (4 k + 14) = 10 k - 2 (k - 7)$

Step 1

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$10 k - 2 (k - 7) = 3 (4 k + 14)$

Step 2

Simplify $10 k - 2 (k - 7)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$10 k - 2 k - 2 \cdot - 7 = 3 (4 k + 14)$

Step 2.1.2

Multiply $- 2$ by $- 7$ .

$10 k - 2 k + 14 = 3 (4 k + 14)$

Step 2.2

Subtract $2 k$ from $10 k$ .

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

Step 3

Simplify $3 (4 k + 14)$ .

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply.

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Step 3.2.1

Multiply $4$ by $3$ .

$8 k + 14 = 12 k + 3 \cdot 14$

Step 3.2.2

Multiply $3$ by $14$ .

$8 k + 14 = 12 k + 42$

Step 4

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

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Step 4.1

Subtract $12 k$ from both sides of the equation.

$8 k + 14 - 12 k = 42$

Step 4.2

Subtract $12 k$ from $8 k$ .

$- 4 k + 14 = 42$

Step 5

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

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Step 5.1

Subtract $14$ from both sides of the equation.

$- 4 k = 42 - 14$

Step 5.2

Subtract $14$ from $42$ .

$- 4 k = 28$

Step 6

Divide each term in $- 4 k = 28$ by $- 4$ and simplify.

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Step 6.1

Divide each term in $- 4 k = 28$ by $- 4$ .

$\frac{- 4 k}{- 4} = \frac{28}{- 4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 4 k}{- 4} = \frac{28}{- 4}$

Step 6.2.1.2

Divide $k$ by $1$ .

$k = \frac{28}{- 4}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $28$ by $- 4$ .

$k = - 7$