Finite Math Examples

$4 - (- 7 - k) > 2 (k + 3)$

Step 1

Simplify $4 - (- 7 - k)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 - - 7 - - k > 2 (k + 3)$

Step 1.1.2

Multiply $- 1$ by $- 7$ .

$4 + 7 - - k > 2 (k + 3)$

Step 1.1.3

Multiply $- - k$ .

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Step 1.1.3.1

Multiply $- 1$ by $- 1$ .

$4 + 7 + 1 k > 2 (k + 3)$

Step 1.1.3.2

Multiply $k$ by $1$ .

$4 + 7 + k > 2 (k + 3)$

Step 1.2

Add $4$ and $7$ .

$11 + k > 2 (k + 3)$

Step 2

Simplify $2 (k + 3)$ .

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Step 2.1

Apply the distributive property.

$11 + k > 2 k + 2 \cdot 3$

Step 2.2

Multiply $2$ by $3$ .

$11 + k > 2 k + 6$

Step 3

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

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Step 3.1

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

$11 + k - 2 k > 6$

Step 3.2

Subtract $2 k$ from $k$ .

$11 - k > 6$

Step 4

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

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Step 4.1

Subtract $11$ from both sides of the inequality.

$- k > 6 - 11$

Step 4.2

Subtract $11$ from $6$ .

$- k > - 5$

Step 5

Divide each term in $- k > - 5$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- k > - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- k}{- 1} < \frac{- 5}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{k}{1} < \frac{- 5}{- 1}$

Step 5.2.2

Divide $k$ by $1$ .

$k < \frac{- 5}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 5$ by $- 1$ .

$k < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$k < 5$

Interval Notation:

$(- \infty, 5)$