Solve the Inequality for w -5+2(-5w+7)>=-5w-10+7

$- 5 + 2 (- 5 w + 7) \geq - 5 w - 10 + 7$

Simplify $- 5 + 2 (- 5 w + 7)$ .

Simplify each term.

Apply the distributive property.

$- 5 + 2 (- 5 w) + 2 \cdot 7 \geq - 5 w - 10 + 7$

Multiply $- 5$ by $2$ .

$- 5 - 10 w + 2 \cdot 7 \geq - 5 w - 10 + 7$

Multiply $2$ by $7$ .

$- 5 - 10 w + 14 \geq - 5 w - 10 + 7$

Add $- 5$ and $14$ .

$- 10 w + 9 \geq - 5 w - 10 + 7$

Add $- 10$ and $7$ .

$- 10 w + 9 \geq - 5 w - 3$

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

Add $5 w$ to both sides of the inequality.

$- 10 w + 9 + 5 w \geq - 3$

Add $- 10 w$ and $5 w$ .

$- 5 w + 9 \geq - 3$

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

Subtract $9$ from both sides of the inequality.

$- 5 w \geq - 3 - 9$

Subtract $9$ from $- 3$ .

$- 5 w \geq - 12$

Divide each term in $- 5 w \geq - 12$ by $- 5$ and simplify.

Divide each term in $- 5 w \geq - 12$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 w}{- 5} \leq \frac{- 12}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 w}{- 5} \leq \frac{- 12}{- 5}$

Divide $w$ by $1$ .

$w \leq \frac{- 12}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$w \leq \frac{12}{5}$

The result can be shown in multiple forms.

Inequality Form:

$w \leq \frac{12}{5}$

Interval Notation:

$(- \infty, \frac{12}{5}]$

Solve the Inequality for w -5+2(-5w+7)>=-5w-10+7

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