What are the solutions of the inequality? Graph the solution.|2x| ≥ 14(1 point)Responses–10 to 10 number lineImage with alt text: –10 to 10 number line–10 to 10 number lineImage with alt text: –10 to 10 number line–10 to 10 number lineImage with alt text: –10 to 10 number line–10 to 10 number line

Answer 1

To solve the inequality |2x| ≥ 14, we need to consider two cases: when 2x is positive and when 2x is negative.

Case 1: 2x ≥ 14
Divide both sides of the inequality by 2 to isolate x:
x ≥ 7

Case 2: -2x ≥ 14
Divide both sides of the inequality by -2, but remember to flip the inequality symbol when dividing by a negative number:
x ≤ -7

Therefore, the solution to the inequality |2x| ≥ 14 is x ≤ -7 or x ≥ 7.

To graph this on a number line, we mark -7 and 7 with closed circles (to indicate that they are included in the solution), and shade the numbers to the left of -7 and to the right of 7.

Here is the number line:
Image: [-10, -9, -8, -7, ●, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, ●, 8, 9, 10]

The shaded regions are to the left of -7 and to the right of 7.