graph the inequality

Question

Solve each inequality.Graph the solution.

2|z+3|-1<1

Answer 1

Given inequality is

Answer 2

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

Add 1 to each side.

2| z + 3 | < 2

Divide each side by 2.

| z + 3 | < 1.

Then, the inequality is | z + 3 |  < 1.

The absolute value inequality | z + 3 |  < 1 is equivalent to - 1 < (z + 3) < 1 or

(z + 3) > - 1 and (z + 3) < 1.

Case 1 :

Solve the inequality (z + 3) > - 1 for z

z + 3 > - 1

z > - 1 - 3

⇒ z > - 4.

Case 2 :

Solve the inequality (z + 3) < 1 for z

z + 3 < 1

z < 1 - 3

⇒ z < - 2.

The solution set is { z Є R | z > - 4 and z < - 2}.

Graph of the solution set on a number line :

Observe the graph , the open circle means that - 2 and - 4 are not the solutions of the inequality.

Comments

Your solution is correct.

But you indicate x instead of z in the numberline.