Pt1420 Unit 1 Lab Report

When given two equations the goal is to make the equations equivalent to one another. These two equations are equivalent. Two equations are known to be equivalent if they have the same solution set. A solution set is a set of numbers that that solve an algebraic equation. In the first equation, the solution set is {5}. In the second solution set both sides of the equation must be equal. Equal means that both sides are balanced. The equality of addition property states that each side of the equal sign must have the exact same numerical value. On both sides, we have a which is the same “number” or “letter”. Since 5 is on one of the sides 5 must be on the other side due to the equality of addition property. That makes x {5}. Finally, because both of their solution sets are {5}, we know that the two equations are equivalent because they have the same solution set.
For these equations to be equivalent there is one condition you must put on any real number a. The condition that must be put on a is that a cannot be 0. The main reason that a cannot be 0 is because when we substitute 0 for a in the second equation you must multiply x times 0. X times 0 is 0. Then when you put 0 in for a on the other side of the equation you must multiply 0 and 2. 0 times 2 also equals 0. So, you get a solution set of {0}. When you compare that to the first solution set it is not the same. The first solution set is {2}. A solution set of {0} is different from a solution set of {2} making the two equations not equivalent. So a can be any real non-zero number. A can be any real non-zero number because of the multiplicative property of equality. That property states that if you multiply both sides of the equation by an integer they will stay