Math Snap

STEP 1

Assumptions1. The given inequalities are $\frac{g-}{4} \geq$ and $\frac{g-11}{3}<-3$
. We need to solve for $g$ in both inequalities3. We need to graph the solution

STEP 2

Let's start by solving the first inequality $\frac{g-2}{4} \geq2$. We can do this by multiplying both sides of the inequality by4.
$$4 \cdot \frac{g-2}{4} \geq4 \cdot2$$

STEP 3

implify the left side of the inequality by cancelling out the's.
$$g-2 \geq \cdot2$$

STEP 4

implify the right side of the inequality.
$$g-2 \geq8$$

STEP 5

Now, to isolate $g$, add2 to both sides of the inequality.
$$g-2+2 \geq8+2$$

STEP 6

implify both sides of the inequality.
$$g \geq10$$

STEP 7

Now let's solve the second inequality $\frac{g-11}{3}<-3$. We can do this by multiplying both sides of the inequality by3.
$$3 \cdot \frac{g-11}{3} <3 \cdot -3$$

STEP 8

implify the left side of the inequality by cancelling out the3's.
$$g-11 <3 \cdot -3$$

STEP 9

implify the right side of the inequality.
$$g-11 < -9$$

STEP 10

Now, to isolate $g$, add to both sides of the inequality.
$$g-+ < -9+$$

STEP 11

implify both sides of the inequality.
$$g <$$

STEP 12

Now we have the solutions for the inequalities $g \geq10$ and $g <2$.

STEP 13

To graph these solutions, we plot them on a number line. We plot $2$ and $10$ as the endpoints.

STEP 14

Since $g <2$, we draw an open circle at $2$ and a line extending to the left, indicating all numbers less than $2$.

Since $g \geq10$, we draw a closed circle at $10$ and a line extending to the right, indicating all numbers greater than or equal to $10$.
The solution to the inequalities is $g \geq10$ or $g <2$.