Solve in ineqand graph the solution set. Write the solution set I. (A) set builder notation and (B) interval notation. 4z+6>14

Let's solve the inequality \( 4z + 6 > 14 \) step-by-step and graph the solution set. We'll also express the solution in both set builder notation and interval notation.

### Step 1: Solve the inequality

\[
4z + 6 > 14
\]

Subtract 6 from both sides:

\[
4z > 8
\]

Next, divide both sides by 4:

\[
z > 2
\]

### Step 2: Solution set
The solution is \( z > 2 \), meaning \( z \) can take any value greater than 2.

### (A) Set Builder Notation:
The solution set in set builder notation is:

\[
\{ z \mid z > 2 \}
\]

### (B) Interval Notation:
The solution set in interval notation is:

\[
(2, \infty)
\]

### Step 3: Graph the solution
To graph this inequality:

1. Draw a number line.
2. Mark the point \( z = 2 \) with an open circle because 2 is not included in the solution.
3. Shade the region to the right of 2, indicating that all values greater than 2 are part of the solution.

Would you like a detailed graph or further explanation? Also, here are some related questions:

1. How do we solve inequalities involving absolute values?
2. What is the difference between "open circle" and "closed circle" in graphing inequalities?
3. How do we solve inequalities involving quadratic expressions?
4. How can we solve compound inequalities?
5. What happens when we multiply or divide an inequality by a negative number?

**Tip:** Always reverse the inequality sign when you multiply or divide by a negative number!

Solve and graph the solution set. Write the solution set in (A) set builder notation and (B) interval notation. 4z + 6 > 14

Learn how to solve and graph the inequality 4z + 6 > 14. This tutorial covers key algebra concepts, including inequalities, set builder notation, and interval notation. Suitable for students in Grades 6-8, with a step-by-step solution and a detailed graph of the solution set.

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