https://file.aiquickdraw.com/mathbot/file/1730742399988fdfvp17e.jpg

To solve the inequality \( 2x + 16 < 2 \), we’ll go through the steps of isolating \( x \):

1. **Subtract 16 from both sides:**

   \[
   2x + 16 - 16 < 2 - 16
   \]

   This simplifies to:

   \[
   2x < -14
   \]

2. **Divide both sides by 2 to solve for \( x \):**

   \[
   x < -7
   \]

So, the solution to the inequality is:

\[
x < -7
\]

### Inequality Notation
In the "Inequality Notation" box, you should enter:
\[
x < -7
\]

### Graphing the Solution
On the number line provided, you would place an open circle at \( -7 \) (since \( x \) is strictly less than \( -7 \), not equal to it) and shade everything to the left of \( -7 \) to represent all values \( x < -7 \).

Would you like further details on this solution or have any questions?

---

Here are some related questions to further your understanding:

1. How do you solve inequalities with variables on both sides?
2. How does graphing differ when the inequality symbol is \( \leq \) or \( \geq \)?
3. What happens if you divide both sides of an inequality by a negative number?
4. Can you explain why we use an open circle for \( x < -7 \) rather than a closed circle?
5. How would the solution change if the inequality were \( 2x + 16 > 2 \) instead?

**Tip:** Remember that when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol.

Solve the inequality and graph the solution on the line provided: 2x + 16 < 2

Learn how to solve and graph the inequality 2x + 16 < 2 with step-by-step instructions. Understand key algebraic concepts like isolating variables and graphing inequalities on a number line. Ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation