2/3 (3x+9)=-2 (2x+6)​

2/3 (3x+9)=-2 (2x+6)​

The Correct Answer and Explanation is:

To solve the equation (\frac{2}{3}(3x + 9) = -2(2x + 6)), we will follow the steps systematically.

Step 1: Distribute the constants on both sides of the equation.

• On the left side, distribute (\frac{2}{3}) to each term inside the parentheses:
  [
  \frac{2}{3}(3x + 9) = \frac{2}{3} \times 3x + \frac{2}{3} \times 9 = 2x + 6.
  ]
• On the right side, distribute (-2) to each term inside the parentheses:
  [
  -2(2x + 6) = -2 \times 2x + (-2) \times 6 = -4x – 12.
  ]
  Now, the equation becomes:
  [
  2x + 6 = -4x – 12.
  ]

Step 2: Move all terms involving (x) to one side.

To eliminate the (-4x) term from the right side, add (4x) to both sides of the equation:
[
2x + 4x + 6 = -4x + 4x – 12.
]
This simplifies to:
[
6x + 6 = -12.
]

Step 3: Move constant terms to the other side.

Next, subtract 6 from both sides to isolate terms involving (x) on the left side:
[
6x + 6 – 6 = -12 – 6.
]
This simplifies to:
[
6x = -18.
]

Step 4: Solve for (x).

Finally, divide both sides of the equation by 6 to solve for (x):
[
x = \frac{-18}{6} = -3.
]

Final Answer:

The solution to the equation is (x = -3).

Explanation:

To solve this equation, we used the distributive property to simplify both sides and then performed algebraic steps to isolate (x). By following the order of operations and maintaining balance (adding or subtracting terms on both sides), we arrived at the solution. This method of solving linear equations ensures that each operation preserves equality and leads to the correct solution.