Question

T - 8 = 8 - x

a. The equation has one solution: 8
b. A value of x that makes the equation true is -8, which when substituted into the equation and simplified makes the equation turn into 8.
c. A value of x that makes the equation false is unknown.

Answer 1

The equation T - 8 = 8 - x has one solution, which is x = 8. To solve for x, we rearrange the equation by subtracting T and multiplying both sides by -1. Substituting a value other than 8 for x can show if the equation is false.

Step-by-step explanation:

To solve the equation T - 8 = 8 - x, we will rearrange the equation to solve for x. We will start by subtracting T from both sides which gives us -8 = -x. To solve for x, we will then multiply both sides by -1 resulting in x = 8. This means that the equation is true when x is 8, which is the one solution of the equation. To check if a value makes the equation false, we can substitute any number other than 8 for x and if the equation does not balance, then the value is not a solution.

For example, if x is -8, substituting it into the equation results in T - 8 = 8 - (-8), simplifying to T -8 = 16, which, when rearranged, does not lead to 8. Thus, -8 is a value that makes the given equation false. Remember to always perform the same operations on both sides of the equation to maintain equality.