graph the inequality

Question

Solve each inequality.Graph the solution.

|2z+2|-1>3

Answer 1

Given inequality is

 

Comments

The solution set of |2z + 2| - 1 > 3 is { z Є R | z > 1 or z < - 3}.

Answer 2

The Absolute Value Inequality is |2z + 2| - 1 > 3.

Add 1 to each side.

|2z + 2| > 4

Divide each side by 2.

| z + 1 | > 2.

The absolute value inequality | z + 1 | > 2 is equivalent to - 2 > (z + 1) > 2 or

(z + 1) < - 2 or (z + 1) > 2.

Case 1 :

Solve the inequality (z + 1) < - 2 for z

z + 1 < - 2

z < - 2 - 1

⇒ z < - 3.

Case 2 :

Solve the inequality (z + 1) > 2 for z

z + 1 > 2

z > 2 - 1

⇒ z > 1.

The solution set is { z Є R | z > 1 or z < - 3}.

Graph of the solution set on a number line :

Observe the graph , the open circle means that - 3 and 1 are not the solutions of the inequality.