Solve the inequality. (Enter your answer using interval notation.) x + 16x + 2 − 3 ≥ 0

1. Break Down the Problem

We need to solve the inequality $x + 16x + 2 - 3 \geq 0$. First, we need to combine like terms and simplify the expression.

2. Relevant Concepts

The inequality can be represented as:

$x + 16x + 2 - 3 = 17x - 1 \geq 0$

3. Analysis and Detail

To solve the inequality $17x - 1 \geq 0$, we can follow these steps:

1. Isolate $x$: $17x \geq 1$
2. Divide both sides by 17: $x \geq \frac{1}{17}$

4. Verify and Summarize

The solution to the inequality is $x \geq \frac{1}{17}$. This means that any value of $x$ that is greater than or equal to $\frac{1}{17}$ satisfies the inequality.

Final Answer

In interval notation, the solution is:

$\left[ \frac{1}{17}, \infty \right)$