Question

consider the following inequality:
$-\frac{2}{3}x + 9 > \frac{2}{3}x + 17$
step 2 of 2 : graph the solution to the given inequality
answer
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pressing the buttons will create an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed intervals, use the clear button. to indicate infinity or negative infinity, drag an open end point to the end of the number line.
number line with -∞, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, ∞

Explanation:

Step1: Solve the inequality

$$\begin{align*} -\frac{2}{3}x + 9 &> \frac{2}{3}x+17\\ -\frac{2}{3}x-\frac{2}{3}x&>17 - 9\\ -\frac{4}{3}x&>8\\ x&<8\times(-\frac{3}{4})\\ x&<- 6 \end{align*}$$

Answer:

The solution of the inequality is \(x < - 6\). On the number - line, we use an open circle at \(x = - 6\) (because the inequality is strict, \(x
eq - 6\)) and shade the part of the number - line to the left of \(x=-6\) towards \(-\infty\).