Question

show what you know linear inequalities
given the inequality ( 3 x - 2 ( x + 4 ) geq 3 x - ( 4 x + 9 ) ), state if the given graph is correct. if not, explain how you would change it.

yes because i can solve all the box

Explanation:

Step1: Simplify the inequality

$$\begin{align*} 3x-2(x + 4)&\geq3x-(4x + 9)\\ 3x-2x-8&\geq3x-4x - 9\\ x-8&\geq -x-9 \end{align*}$$

Step2: Solve for \(x\)

Add \(x\) to both sides:
$$x-8+x\geq -x-9+x$$
$$2x-8\geq - 9$$
Add \(8\) to both sides:
$$2x-8 + 8\geq -9+8$$
$$2x\geq -1$$
Divide both sides by \(2\):
$$x\geq-\frac{1}{2}$$

Answer:

The given graph is not correct. The correct graph should have a closed - circle at \(-\frac{1}{2}\) (since the inequality is \(x\geq-\frac{1}{2}\)) and the arrow should point to the right.