−2(−2x−2)<2x−6−2(−2𝑥−2)<2𝑥−6Step 2 of 2 :  Graph the solution to the given inequality.

Step 1: Break Down the Problem

We are given the compound inequality: $-2(-2x - 2) < 2x - 6 - 2(-2x - 2) < 2x - 6$ We will break it down into two parts and solve them individually.

Step 2: Relevant Concepts

Let's simplify each part of the inequality.

1. Part 1: $-2(-2x - 2) < 2x - 6 - 2(-2x - 2)$
2. Part 2: $2x - 6 < 2x - 6$ (this part will be checked for contradictions or validity)

Step 3: Analysis and Detail

Part 1: Solve the first part

1. Expand $-2(-2x - 2)$: $4x + 4$

2. Expand $-2(-2x - 2)$ again in the second position: $4x + 4$

3. The inequality becomes: $4x + 4 < 2x - 6 + 4x + 4$ Which simplifies to: $4x + 4 < 2x + 2$

4. Rearranging gives: $4x - 2x < 2 - 4$ Thus: $2x < -2$ Solving for $x$: $x < -1$

Part 2: Check the second part

1. The second part is simply: $2x - 6 < 2x - 6$ This statement is false since it implies $0 < 0$.

Since the second part doesn’t yield any solution, we only have the valid solution from Part 1.

Step 4: Verify and Summarize

We found:

1. From Part 1, $x < -1$.
2. Part 2 does not contribute any further restrictions or valid solutions.

Final Answer

The solution to the inequality is: $x < -1$ To graph this solution on a number line, represent all values to the left of $-1$ with an open circle (indicating $-1$ itself is not included).