https://file.aiquickdraw.com/mathbot/file/1725555560416sq7bd109.jpg

Let's solve the inequality step by step using the addition and multiplication principles, as the problem requires.

The inequality given is:

\[
11x - 10 < -43
\]

### Step 1: Add 10 to both sides
We want to isolate the term with \(x\), so we start by adding 10 to both sides:

\[
11x - 10 + 10 < -43 + 10
\]

Simplifying:

\[
11x < -33
\]

### Step 2: Divide both sides by 11
Now, divide both sides by 11 to solve for \(x\):

\[
x < \frac{-33}{11}
\]

Simplifying:

\[
x < -3
\]

### Conclusion:
The solution to the inequality is \(x < -3\).

Now, let's look at the choices:

- **A**: The solution set is \(\{ x \mid x \geq \}\)
- **B**: The solution set is \(\{ x \mid x < \}\)
- **C**: The solution set is \(\{ x \mid x > \}\)
- **D**: The solution set is \(\{ x \mid x \leq \}\)

The correct answer corresponds to choice **B**, where \(x < -3\).

Would you like more details or have any questions?

Here are five related questions for you to consider:
1. How would the inequality change if the \(11x - 10\) were on the right side instead?
2. What happens when multiplying or dividing inequalities by negative numbers?
3. How do you graph the solution \(x < -3\) on a number line?
4. Can you solve a similar inequality where the \(x\)-term has a fractional coefficient?
5. How would the solution change if the inequality was \(11x - 10 > -43\)?

**Tip**: Always reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Solve the inequality 11x - 10 < -43 using the addition and multiplication principles.

Learn how to solve the linear inequality 11x - 10 < -43 step by step. This problem covers key algebra concepts such as inequality manipulation using addition and division principles. Suitable for 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