Solve the Inequality for w -6(w+1)<2(w+5)

$- 6 (w + 1) < 2 (w + 5)$

Step 1

Simplify $- 6 (w + 1)$ .

Start simplifying.

$0 + 0 - 6 (w + 1) < 2 (w + 5)$

Simplify by adding zeros.

$- 6 (w + 1) < 2 (w + 5)$

Apply the distributive property.

$- 6 w - 6 \cdot 1 < 2 (w + 5)$

Multiply $- 6$ by $1$ .

$- 6 w - 6 < 2 (w + 5)$

Step 2

Simplify $2 (w + 5)$ .

Apply the distributive property.

$- 6 w - 6 < 2 w + 2 \cdot 5$

Multiply $2$ by $5$ .

$- 6 w - 6 < 2 w + 10$

Step 3

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

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

$- 6 w - 6 - 2 w < 10$

Subtract $2 w$ from $- 6 w$ .

$- 8 w - 6 < 10$

Step 4

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

Add $6$ to both sides of the inequality.

$- 8 w < 10 + 6$

Add $10$ and $6$ .

$- 8 w < 16$

Step 5

Divide each term in $- 8 w < 16$ by $- 8$ and simplify.

Divide each term in $- 8 w < 16$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 w}{- 8} > \frac{16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 w}{- 8} > \frac{16}{- 8}$

Divide $w$ by $1$ .

$w > \frac{16}{- 8}$

Simplify the right side.

Divide $16$ by $- 8$ .

$w > - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$w > - 2$

Interval Notation:

$(- 2, \infty)$

Solve the Inequality for w -6(w+1)<2(w+5)

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