Solve for w 42w>2(w+7)

$42 w > 2 (w + 7)$

Step 1

Simplify $2 (w + 7)$ .

Apply the distributive property.

$42 w > 2 w + 2 \cdot 7$

Multiply $2$ by $7$ .

$42 w > 2 w + 14$

Step 2

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

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

$42 w - 2 w > 14$

Subtract $2 w$ from $42 w$ .

$40 w > 14$

Step 3

Divide each term in $40 w > 14$ by $40$ and simplify.

Divide each term in $40 w > 14$ by $40$ .

$\frac{40 w}{40} > \frac{14}{40}$

Simplify the left side.

Cancel the common factor of $40$ .

Cancel the common factor.

$\frac{40 w}{40} > \frac{14}{40}$

Divide $w$ by $1$ .

$w > \frac{14}{40}$

Simplify the right side.

Cancel the common factor of $14$ and $40$ .

Factor $2$ out of $14$ .

$w > \frac{2 (7)}{40}$

Cancel the common factors.

Factor $2$ out of $40$ .

$w > \frac{2 \cdot 7}{2 \cdot 20}$

Cancel the common factor.

$w > \frac{2 \cdot 7}{2 \cdot 20}$

Rewrite the expression.

$w > \frac{7}{20}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w > \frac{7}{20}$

Interval Notation:

$(\frac{7}{20}, \infty)$