Solve for w 5(5-w)-7(7+w)<0

$5 (5 - w) - 7 (7 + w) < 0$

Step 1

Simplify $5 (5 - w) - 7 (7 + w)$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 5 + 5 (- w) - 7 (7 + w) < 0$

Multiply $5$ by $5$ .

$25 + 5 (- w) - 7 (7 + w) < 0$

Multiply $- 1$ by $5$ .

$25 - 5 w - 7 (7 + w) < 0$

Apply the distributive property.

$25 - 5 w - 7 \cdot 7 - 7 w < 0$

Multiply $- 7$ by $7$ .

$25 - 5 w - 49 - 7 w < 0$

Simplify by adding terms.

Subtract $49$ from $25$ .

$- 5 w - 24 - 7 w < 0$

Subtract $7 w$ from $- 5 w$ .

$- 12 w - 24 < 0$

Step 2

Add $24$ to both sides of the inequality.

$- 12 w < 24$

Step 3

Divide each term in $- 12 w < 24$ by $- 12$ and simplify.

Divide each term in $- 12 w < 24$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 w}{- 12} > \frac{24}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 w}{- 12} > \frac{24}{- 12}$

Divide $w$ by $1$ .

$w > \frac{24}{- 12}$

Simplify the right side.

Divide $24$ by $- 12$ .

$w > - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w > - 2$

Interval Notation:

$(- 2, \infty)$

Solve for w 5(5-w)-7(7+w)<0

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