Solve the Inequality for g -2g+4<=-6g-9

$- 2 g + 4 \leq - 6 g - 9$

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

Add $6 g$ to both sides of the inequality.

$- 2 g + 4 + 6 g \leq - 9$

Add $- 2 g$ and $6 g$ .

$4 g + 4 \leq - 9$

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

Subtract $4$ from both sides of the inequality.

$4 g \leq - 9 - 4$

Subtract $4$ from $- 9$ .

$4 g \leq - 13$

Divide each term in $4 g \leq - 13$ by $4$ and simplify.

Divide each term in $4 g \leq - 13$ by $4$ .

$\frac{4 g}{4} \leq \frac{- 13}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 g}{4} \leq \frac{- 13}{4}$

Divide $g$ by $1$ .

$g \leq \frac{- 13}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$g \leq - \frac{13}{4}$

The result can be shown in multiple forms.

Inequality Form:

$g \leq - \frac{13}{4}$

Interval Notation:

$(- \infty, - \frac{13}{4}]$