Final answer:
When an equation is an identity, it is true for all values of x, and thus the solution for x is all real numbers. To verify if an equation is an identity, simplify it and check if it holds true irrespective of the value of x.
Step-by-step explanation:
The question asks, what do I write for x= when an equation is an identity? An equation is an identity when it is true for all values of x. In the example provided, 4(6x+2)+3(3x+3)+6=, if we simplify it and it turns out to be true regardless of the x-value, then it is an identity equation. Hence, the answer for x would be all real numbers since the equation is true for every x.
To solve an equation and determine whether it's an identity, follow these steps:
- Identify the knowns and unknowns.
- Choose an appropriate equation.
- Rearrange the equation to solve for the unknown, x.
- Simplify the equation significantly if necessary.
- After simplification, if we find that the equation holds for all x, then x can be any real number.
It should be noted that if after step 4 the equation does not simplify to a true statement for all x, then it is not an identity, and specific solutions for x must be found.
To find the value of x when an equation is an identity, we need to simplify the equation and see if it becomes true for all values of x. Let's simplify the given equation:
4(6x+2)+3(3x+3)+6=
24x+8+9x+9+6=
33x+23=
This equation is an identity because no matter what value we substitute for x, the equation will always be true. Therefore, x can take any value.