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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

Question

Solve for x.

2(2x2)+x+2=9-2(-2x - 2) + x + 2 = -9

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Solution

1. Break Down the Problem

We need to solve the equation: 2(2x2)+x+2=9 -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 x .

3. Analysis and Detail

  1. Distribute 2-2 in the term 2(2x2)-2(-2x - 2): 2(2x)2(2)=4x+4 -2(-2x) - 2(-2) = 4x + 4 So, the equation now becomes: 4x+4+x+2=9 4x + 4 + x + 2 = -9

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

  3. To isolate x x , subtract 6 6 from both sides: 5x=96 5x = -9 - 6 Which results in: 5x=15 5x = -15

  4. Finally, divide both sides by 5 5 : x=155=3 x = \frac{-15}{5} = -3

4. Verify and Summarize

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

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

Calculating: 2(62)3+2=9 -2(6 - 2) - 3 + 2 = -9 2(4)3+2=9 -2(4) - 3 + 2 = -9 83+2=9 -8 - 3 + 2 = -9 9=9 -9 = -9

The verification shows that the solution is correct.

Final Answer

x=3 x = -3

This problem has been solved

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