Solve the Inequality for g 3(7g+17)>-19+14g

$3 (7 g + 17) > - 19 + 14 g$

Simplify $3 (7 g + 17)$ .

Rewrite.

$0 + 0 + 3 (7 g + 17) > - 19 + 14 g$

Simplify by adding zeros.

$3 (7 g + 17) > - 19 + 14 g$

Apply the distributive property.

$3 (7 g) + 3 \cdot 17 > - 19 + 14 g$

Multiply.

Multiply $7$ by $3$ .

$21 g + 3 \cdot 17 > - 19 + 14 g$

Multiply $3$ by $17$ .

$21 g + 51 > - 19 + 14 g$

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

Subtract $14 g$ from both sides of the inequality.

$21 g + 51 - 14 g > - 19$

Subtract $14 g$ from $21 g$ .

$7 g + 51 > - 19$

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

Subtract $51$ from both sides of the inequality.

$7 g > - 19 - 51$

Subtract $51$ from $- 19$ .

$7 g > - 70$

Divide each term in $7 g > - 70$ by $7$ and simplify.

Divide each term in $7 g > - 70$ by $7$ .

$\frac{7 g}{7} > \frac{- 70}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 g}{7} > \frac{- 70}{7}$

Divide $g$ by $1$ .

$g > \frac{- 70}{7}$

Simplify the right side.

Divide $- 70$ by $7$ .

$g > - 10$

The result can be shown in multiple forms.

Inequality Form:

$g > - 10$

Interval Notation:

$(- 10, \infty)$