Solve for x.minus, 2, left parenthesis, minus, 2, x, minus, 2, right parenthesis, plus, x, plus, 2, equals, minus, 9−2(−2x−2)+x+2=−9

1. Break Down the Problem

We need to solve the equation: $-2(-2x - 2) + x + 2 = -9$

2. Relevant Concepts

We will apply the distributive property and basic algebraic principles to solve the equation for $x$.

3. Analysis and Detail

1. Distribute $-2$ in the term $-2(-2x - 2)$: $-2(-2x) - 2(-2) = 4x + 4$ So, the equation now becomes: $4x + 4 + x + 2 = -9$

2. Combine like terms: $(4x + x) + (4 + 2) = -9$ This simplifies to: $5x + 6 = -9$

3. To isolate $x$, subtract $6$ from both sides: $5x = -9 - 6$ Which results in: $5x = -15$

4. Finally, divide both sides by $5$: $x = \frac{-15}{5} = -3$

4. Verify and Summarize

Now, let’s verify our solution by substituting $x = -3$ back into the original equation:

$-2(-2(-3) - 2) + (-3) + 2 = -9$

Calculating: $-2(6 - 2) - 3 + 2 = -9$ $-2(4) - 3 + 2 = -9$ $-8 - 3 + 2 = -9$ $-9 = -9$

The verification shows that the solution is correct.

Final Answer

$x = -3$