When solving the equation 5( x + 6 ) - 2x = 3( x + 10 ), it simplifies to an identity, indicating that any real number satisfies the equation, hence there is no unique solution for x.
To solve for x in the equation 5( x + 6 ) - 2x = 3( x + 10 ), start by expanding both sides of the equation:
- Multiply 5 times both x and 6 to get 5x + 30.
- Multiply 3 times both x and 10 to get 3x + 30.
Next, combine like terms and simplify:
- Subtract 2x from 5x on the left side to get 3x + 30.
- As both sides have a +30, subtract 30 from both sides to eliminate the constant.
- You are left with 3x = 3x, which indicates that x can be any number.
In conclusion, we find that the equation is an identity, meaning that any real number for x satisfies the equation, so there is no unique solution.