Solve 2/3(6x+30) = x+5(x+4)-2x and please show me the steps?

2/3(6x+30) = x+5(x+4)-2x

4x + 20 = x + 5x + 20 - 2x
4x - 5x + 2x = 20 - 20
x=0

Thank you a lot!

To solve the equation 2/3(6x + 30) = x + 5(x + 4) - 2x, let's go through the steps:

Step 1: Distribute the terms inside the parentheses on both sides of the equation:
2/3 * 6x + 2/3 * 30 = x + 5x + 5 * 4 - 2x

Simplifying the expression gives us:
4x + 20 = x + 5x + 20 - 2x

Step 2: Combine like terms on both sides of the equation:
4x + 20 = x + 5x + 20 - 2x
4x + 20 = 4x + 20

Step 3: Subtract 4x from both sides of the equation:
4x - 4x + 20 = 4x - 4x + 20
20 = 20

Step 4: Simplify both sides. Since the equation is true, it indicates that the equation is an identity, which means it is true for all values of x.

So, the solution to the equation is x can be any real number.

To solve the equation 2/3(6x + 30) = x + 5(x + 4) - 2x, you can follow these steps:

Step 1: Distribute the coefficients across each term inside the parentheses on both sides of the equation.
(2/3)(6x) + (2/3)(30) = x + (5)(x) + (5)(4) - 2x
(4x + 20) = x + 5x + 20 - 2x

Step 2: Combine like terms on both sides of the equation.
4x + 20 = x + 5x + 20 - 2x
4x + 20 = 4x + 20

Step 3: Move all terms containing x to one side of the equation by subtracting 4x from both sides.
4x + 20 - 4x = x + 5x + 20 - 2x - 4x
20 = x + 5x + 20 - 2x - 4x

Step 4: Simplify and combine like terms on both sides of the equation.
20 = x + 5x + 20 - 2x - 4x
20 = 0

Step 5: Perform any necessary algebraic simplifications.
20 = 0 (This equation is not possible because 20 cannot equal 0.)

Step 6: Conclusion
The equation 2/3(6x + 30) = x + 5(x + 4) - 2x has no solutions.

It is important to double-check your work after solving the equation and make sure that the solution holds true when substituted back into the original equation.