Solve the Inequality for w 12+10w>=8(w+12)

$12 + 10 w \geq 8 (w + 12)$

Step 1

Simplify $8 (w + 12)$ .

Rewrite.

$12 + 10 w \geq 0 + 0 + 8 (w + 12)$

Simplify by adding zeros.

$12 + 10 w \geq 8 (w + 12)$

Apply the distributive property.

$12 + 10 w \geq 8 w + 8 \cdot 12$

Multiply $8$ by $12$ .

$12 + 10 w \geq 8 w + 96$

Step 2

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

Subtract $8 w$ from both sides of the inequality.

$12 + 10 w - 8 w \geq 96$

Subtract $8 w$ from $10 w$ .

$12 + 2 w \geq 96$

Step 3

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

Subtract $12$ from both sides of the inequality.

$2 w \geq 96 - 12$

Subtract $12$ from $96$ .

$2 w \geq 84$

Step 4

Divide each term in $2 w \geq 84$ by $2$ and simplify.

Divide each term in $2 w \geq 84$ by $2$ .

$\frac{2 w}{2} \geq \frac{84}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 w}{2} \geq \frac{84}{2}$

Divide $w$ by $1$ .

$w \geq \frac{84}{2}$

Simplify the right side.

Divide $84$ by $2$ .

$w \geq 42$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$w \geq 42$

Interval Notation:

$[42, \infty)$