To solve the inequality [tex]\(4x \geq 16\)[/tex], we will go through the steps one by one.
1. Start with the given inequality:
[tex]\[
4x \geq 16
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex] by dividing both sides of the inequality by 4. This step is to ensure that the coefficient of [tex]\(x\)[/tex] is 1.
[tex]\[
\frac{4x}{4} \geq \frac{16}{4}
\][/tex]
3. Simplify the division:
[tex]\[
x \geq 4
\][/tex]
Thus, the solution to the inequality is:
[tex]\[
x \geq 4
\][/tex]
Which corresponds to option B.
### Graphing the Inequality
To graph the inequality [tex]\(x \geq 4\)[/tex]:
1. Draw a number line.
2. Locate the number 4 on the number line and make a solid circle at 4. A solid circle indicates that 4 is included in the solution set (because the inequality is "greater than or equal to").
3. Shade the region to the right of 4. This shading represents all numbers greater than or equal to 4.
The number line will look like this:
[tex]\[
\begin{array}{c}
\ \ \ \ \ \ \ \ \ \ \ \ 4 \rightarrow \text{ solid circle} \\
\dots \quad \quad \quad \ \ \ 3 \ \ \ 4 \ \ \ 5 \ \ \dots \quad \quad \\
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \uparrow \quad \rightarrow \text{ shaded region}
\end{array}
\][/tex]
Thus, the correct answer is:
[tex]\[
\textbf{B. } x \geq 4
\][/tex]
