Algebra Examples

$- 7 (k + 5) = 3 k - (8 k - 1)$

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.

$3 k - (8 k - 1) = - 7 (k + 5)$

Step 2

Simplify $3 k - (8 k - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 k - (8 k) - - 1 = - 7 (k + 5)$

Step 2.1.2

Multiply $8$ by $- 1$ .

$3 k - 8 k - - 1 = - 7 (k + 5)$

Step 2.1.3

Multiply $- 1$ by $- 1$ .

$3 k - 8 k + 1 = - 7 (k + 5)$

Step 2.2

Subtract $8 k$ from $3 k$ .

$- 5 k + 1 = - 7 (k + 5)$

Step 3

Simplify $- 7 (k + 5)$ .

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Step 3.1

Apply the distributive property.

$- 5 k + 1 = - 7 k - 7 \cdot 5$

Step 3.2

Multiply $- 7$ by $5$ .

$- 5 k + 1 = - 7 k - 35$

Step 4

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

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Step 4.1

Add $7 k$ to both sides of the equation.

$- 5 k + 1 + 7 k = - 35$

Step 4.2

Add $- 5 k$ and $7 k$ .

$2 k + 1 = - 35$

Step 5

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

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Step 5.1

Subtract $1$ from both sides of the equation.

$2 k = - 35 - 1$

Step 5.2

Subtract $1$ from $- 35$ .

$2 k = - 36$

Step 6

Divide each term in $2 k = - 36$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 k = - 36$ by $2$ .

$\frac{2 k}{2} = \frac{- 36}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{- 36}{2}$

Step 6.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 36}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 36$ by $2$ .

$k = - 18$