We have been using the equal sign throughout previous sessions. In this part we are going to look at the meaning of equality, which will give us some insight on using equality and its properties to solve equations. Note 2
Examine the following equations. Each equation makes a statement about quantities. Is each statement true always, sometimes, or never? Think about your reasoning for each statement.
a.
5 + 3 = 8
b.
2 + 14 = 12
c.
5 + 3 = y
d.
x + 3 = y
e.
3x = 2x + x
f.
3x = 3x + 1
Problem A2
If someone asked you to solve the equations in Problem A1, what would the solution sets be?
The definition of a solution set is helpful here. Consider how many different solutions there are in each solution set. Close Tip
Problem A3
A chalkboard reads: 10 + 21 = ?
a.
Replace the "?" with something that makes the equation always true.
b.
Replace the "?" with something that makes the equation always false.
c.
Replace the "?" with something that makes the equation sometimes true and sometimes false.
Problems in Part A are based on The Partners in Change Handbook: A Professional Development Curriculum in Mathematics, developed under the direction of Principal Investigator Suzanne Chapin at Boston University in 1997. Preparation of the handbook supported by the U.S. Department of Education.
