Final answer:
To solve the equation T - 8 = 8 - x, we want to find values of x that make the equation true. When x = -8, the equation holds as T becomes 24, but when x = 8, the resulting statement that 8 = 0 is false therefore, x = -8 is the solution while x = 8 is not.
Step-by-step explanation:
When solving an equation, the aim is to find the value of the unknown variable that makes the equation true. In the case of the equation T - 8 = 8 - x, adding 8 to both sides does not change the equality and we obtain T = 16 - x. To find the value of x that satisfies this equation, we can set x to a given number and determine if the equation holds true. For example, if x is -8, then T - 8 = 8 - (-8) simplifies to T = 16 + 8, which means T = 24; thus, the equation is true with x = -8. However, if x = 8, then T = 16 - 8, which simplifies to T = 8, is not a true statement since the original equation would become 8 = 0, which is false. Hence, x = -8 is a solution to the equation, and x = 8 is not.