Question

directions
select up to 2 number line button(s) below. click to activate and drag the circles on the number line to graph the answer
this question is calculator active.
graph the solution set for ( 3 ( x - 3 ) - 5 x > - 3 x - 6 )
select a ray. move the point on the ray to the correct place on the number line.

Explanation:

Step1: Simplify the inequality

$$\begin{align*} 3(x - 3)-5x&>-3x - 6\\ 3x-9 - 5x&>-3x - 6\\ -2x-9&>-3x - 6 \end{align*}$$

Step2: Add \(3x\) to both sides

$$\begin{align*} -2x + 3x-9&>-3x+ 3x - 6\\ x-9&>-6 \end{align*}$$

Step3: Add 9 to both sides

$$\begin{align*} x-9 + 9&>-6+9\\ x&>3 \end{align*}$$

Since \(x>3\), we use an open - circle at \(x = 3\) and draw a ray to the right.

Answer:

We select the open - circle (top - most button in the left panel) and place it at \(3\) on the number line, then draw a ray to the right.