Solve each of the following equations.

𝑎)𝑥+2+𝑥−2=2 𝑏)4𝑥 −5𝑥 = 2 𝑥−3 𝑥−6

Let's solve each of the given equations step by step.

### a) \( x + 2 + x - 2 = 2 \)

1. Combine like terms on the left side:
   \[
   x + x + 2 - 2 = 2
   \]
   \[
   2x = 2
   \]

2. Divide both sides by 2:
   \[
   x = 1
   \]

The solution for equation (a) is \( x = 1 \).

### b) \( 4x - 5x = 2x - 3x - 6 \)

1. Combine like terms on both sides:
   \[
   -x = -x - 6
   \]

2. Add \( x \) to both sides to eliminate \( -x \) from both sides:
   \[
   -x + x = -x + x - 6
   \]
   \[
   0 = -6
   \]

Since this results in a contradiction (\(0 \neq -6\)), there are no solutions for this equation. Therefore, the equation is inconsistent.

To summarize:

- **Equation (a)** has the solution: \( x = 1 \).
- **Equation (b)** has no solution.

Would you like details or have any questions? Here are five more questions you might want to ask:

1. How do you solve quadratic equations?
2. Can you explain the quadratic formula?
3. How do you solve a system of linear equations using the substitution method?
4. What is the method for completing the square?
5.

Learn how to solve equations step by step: x + 2 + x - 2 = 2 and 4x - 5x = 2x - 3x - 6. Understand the process of combining like terms and solving linear equations. Suitable for Grades 6-8.

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