Algebra Examples

$7 < - (- k - 3) + 2$

Step 1

Rewrite so $k$ is on the left side of the inequality.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- - k - - 3 + 2 > 7$

Step 2.1.2

Multiply $- - k$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 1$ .

$1 k - - 3 + 2 > 7$

Step 2.1.2.2

Multiply $k$ by $1$ .

$k - - 3 + 2 > 7$

Step 2.1.3

Multiply $- 1$ by $- 3$ .

$k + 3 + 2 > 7$

Step 2.2

Add $3$ and $2$ .

$k + 5 > 7$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the inequality.

$k > 7 - 5$

Step 3.2

Subtract $5$ from $7$ .

$k > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$k > 2$

Interval Notation:

$(2, \infty)$