Solve the Inequality for g 5g-2<=3g+8

$5 g - 2 \leq 3 g + 8$

Step 1

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

Subtract $3 g$ from both sides of the inequality.

$5 g - 2 - 3 g \leq 8$

Subtract $3 g$ from $5 g$ .

$2 g - 2 \leq 8$

Step 2

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

Add $2$ to both sides of the inequality.

$2 g \leq 8 + 2$

Add $8$ and $2$ .

$2 g \leq 10$

Step 3

Divide each term in $2 g \leq 10$ by $2$ and simplify.

Divide each term in $2 g \leq 10$ by $2$ .

$\frac{2 g}{2} \leq \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 g}{2} \leq \frac{10}{2}$

Divide $g$ by $1$ .

$g \leq \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$g \leq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$g \leq 5$

Interval Notation:

$(- \infty, 5]$