Algebra Examples

$- 2 (k - 1) > 8 (1 + k)$

Step 1

Simplify $- 2 (k - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (k - 1) > 8 (1 + k)$

Step 1.2

Simplify by adding zeros.

$- 2 (k - 1) > 8 (1 + k)$

Step 1.3

Apply the distributive property.

$- 2 k - 2 \cdot - 1 > 8 (1 + k)$

Step 1.4

Multiply $- 2$ by $- 1$ .

$- 2 k + 2 > 8 (1 + k)$

Step 2

Simplify $8 (1 + k)$ .

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Step 2.1

Apply the distributive property.

$- 2 k + 2 > 8 \cdot 1 + 8 k$

Step 2.2

Multiply $8$ by $1$ .

$- 2 k + 2 > 8 + 8 k$

Step 3

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

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Step 3.1

Subtract $8 k$ from both sides of the inequality.

$- 2 k + 2 - 8 k > 8$

Step 3.2

Subtract $8 k$ from $- 2 k$ .

$- 10 k + 2 > 8$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the inequality.

$- 10 k > 8 - 2$

Step 4.2

Subtract $2$ from $8$ .

$- 10 k > 6$

Step 5

Divide each term in $- 10 k > 6$ by $- 10$ and simplify.

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Step 5.1

Divide each term in $- 10 k > 6$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 k}{- 10} < \frac{6}{- 10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 10 k}{- 10} < \frac{6}{- 10}$

Step 5.2.1.2

Divide $k$ by $1$ .

$k < \frac{6}{- 10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $6$ and $- 10$ .

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Step 5.3.1.1

Factor $2$ out of $6$ .

$k < \frac{2 (3)}{- 10}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $- 10$ .

$k < \frac{2 \cdot 3}{2 \cdot - 5}$

Step 5.3.1.2.2

Cancel the common factor.

$k < \frac{2 \cdot 3}{2 \cdot - 5}$

Step 5.3.1.2.3

Rewrite the expression.

$k < \frac{3}{- 5}$

Step 5.3.2

Move the negative in front of the fraction.

$k < - \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$k < - \frac{3}{5}$

Interval Notation:

$(- \infty, - \frac{3}{5})$