Solve for w -2(w+4)+9<-11

$- 2 (w + 4) + 9 < - 11$

Step 1

Simplify $- 2 (w + 4) + 9$ .

Simplify each term.

Apply the distributive property.

$- 2 w - 2 \cdot 4 + 9 < - 11$

Multiply $- 2$ by $4$ .

$- 2 w - 8 + 9 < - 11$

Add $- 8$ and $9$ .

$- 2 w + 1 < - 11$

Step 2

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

Subtract $1$ from both sides of the inequality.

$- 2 w < - 11 - 1$

Subtract $1$ from $- 11$ .

$- 2 w < - 12$

Step 3

Divide each term in $- 2 w < - 12$ by $- 2$ and simplify.

Divide each term in $- 2 w < - 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 w}{- 2} > \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 w}{- 2} > \frac{- 12}{- 2}$

Divide $w$ by $1$ .

$w > \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$w > 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w > 6$

Interval Notation:

$(6, \infty)$

Solve for w -2(w+4)+9<-11

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