https://file.aiquickdraw.com/mathbot/file/1726707766891jntuj38t.jpg

The equation presented in the image is:

\[
2(-x - 2) = 2(-x - 2)
\]

### Step-by-step Solution:

1. Expand both sides of the equation:
   \[
   2(-x - 2) = -2x - 4
   \]
   So, the equation becomes:
   \[
   -2x - 4 = -2x - 4
   \]

2. The simplified equation is:
   \[
   -2x - 4 = -2x - 4
   \]
   This is an **identity** because both sides are identical. This means that no matter what value of \( x \) is chosen, the equation will always hold true.

### Conclusion:
There are **infinite solutions** to this equation, as both sides are equal for any value of \( x \).

---

Would you like a further breakdown or explanation? Here are 5 follow-up questions you might find useful:

1. What is the difference between an equation with infinite solutions and one with no solution?
2. Can you explain how to recognize when an equation has infinite solutions just by looking at it?
3. How does expanding both sides of an equation help in identifying the solution type?
4. Are there any special cases where such equations could have only one solution?
5. How would the equation change if only one side had a different constant term?

### Tip:
When both sides of an equation are identical after simplification, it always results in infinite solutions.

Solve the following equation for x. Express your answer in the simplest form. If there are infinite solutions state 'infinite solutions' and if there are no solutions state 'no solutions.' 2(-x - 2) = 2(-x - 2).

Discover how to solve the equation 2(-x - 2) = 2(-x - 2), an algebraic identity where both sides are identical. This tutorial covers key concepts like the distributive property and the identity property of equations. Suitable 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