Question

graph the solution set of the following inequality. |2x - 5| > 9 one point graph -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 point 1 solidity point 2 solidity change shading

Explanation:

Step1: Rewrite absolute - value inequality

The absolute - value inequality \(|2x - 5|>9\) can be rewritten as two separate inequalities: \(2x−5 > 9\) or \(2x−5 < - 9\).

Step2: Solve \(2x−5 > 9\)

Add 5 to both sides: \(2x>9 + 5\), so \(2x>14\). Then divide both sides by 2: \(x > 7\).

Step3: Solve \(2x−5 < - 9\)

Add 5 to both sides: \(2x<-9 + 5\), so \(2x<-4\). Then divide both sides by 2: \(x < - 2\).

Step4: Graph the solution

On the number line, we have an open - circle at \(x=-2\) (because \(x
eq - 2\)) and shade to the left of \(x = - 2\). We also have an open - circle at \(x = 7\) (because \(x
eq7\)) and shade to the right of \(x = 7\).

Answer:

The solution set is \(x<-2\) or \(x > 7\). On the number line, we have open - circles at \(x=-2\) and \(x = 7\), and we shade the regions to the left of \(x=-2\) and to the right of \(x = 7\).