https://file.aiquickdraw.com/mathbot/file/17257360512684q480z29.jpg

https://file.aiquickdraw.com/mathbot/file/1725736051268hkl25q2e.jpg

The problem shown in the first image is:

\[
6x - 10 < -22
\]

We will solve this inequality using the addition and multiplication principles:

1. **Addition Principle**: Add 10 to both sides to eliminate the constant term on the left-hand side.
   \[
   6x - 10 + 10 < -22 + 10
   \]
   Simplifying this gives:
   \[
   6x < -12
   \]

2. **Multiplication Principle**: Now, divide both sides by 6 to solve for \(x\).
   \[
   \frac{6x}{6} < \frac{-12}{6}
   \]
   Simplifying this gives:
   \[
   x < -2
   \]

Thus, the solution is \(x < -2\).

Now, looking at the answer choices provided in the second image, the correct choice would be option **A** where \( x < -2 \).

Let me know if you need further details or explanations! Here are five related questions for more practice:

1. How would the solution change if the inequality was \(6x - 10 \leq -22\)?
2. What is the effect of multiplying or dividing an inequality by a negative number?
3. How would you solve the inequality \(6x + 5 < 17\)?
4. What happens if we change the inequality to \(6x - 10 > -22\)?
5. Can you solve the equation \(6x - 10 = -22\) and compare the solution with the inequality?

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

Solve the inequality 6x - 10 < -22 using the addition and multiplication principles.

Learn how to solve the inequality 6x - 10 < -22 using the addition and multiplication principles. This problem is suitable for students in Grades 7-9 and covers key algebraic concepts, including the properties of inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation