Solve for g g+8<=2g+5

$g + 8 \leq 2 g + 5$

Step 1

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

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

$g + 8 - 2 g \leq 5$

Subtract $2 g$ from $g$ .

$- g + 8 \leq 5$

Step 2

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

Subtract $8$ from both sides of the inequality.

$- g \leq 5 - 8$

Subtract $8$ from $5$ .

$- g \leq - 3$

Step 3

Divide each term in $- g \leq - 3$ by $- 1$ and simplify.

Divide each term in $- g \leq - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- g}{- 1} \geq \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{g}{1} \geq \frac{- 3}{- 1}$

Divide $g$ by $1$ .

$g \geq \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$g \geq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$g \geq 3$

Interval Notation:

$[3, \infty)$

Solve for g g+8<=2g+5

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