Changing the Subject

Video 1

Video 1 Explanation


Question 1: If 2a + b + 5 = c, make b the subject
Changing the subject just means we have rearrange the terms so that the subject is what the terms equal. Currently, the subject is c.
What we are actually doing is trying to find what b equals, the same concept of when we were trying to solve for x in a linear equation applies here. (REMEMBER TO TREAT BOTH SIDES EQUALLY)
2a + b + 5 = c
Subtract 5 from both sides
2a + b + 5 - 5 = c - 5
2a + b = c - 5
Subtract 2a from both sides
2a + b - 2a = c - 5 - 2a
b = c - 5 - 2a

Above we subtracted 5 from both sides first, and then subtracted 2a from both sides. Below, we subtracted 2a first, remember as we treated both sides equally, the order of how we treat both sides does not matter. So as seen below, we get the same answer.
2a + b + 5 = c
Subtract 2a from both sides
2a + b - 2a + 5 = c - 2a
b + 5 = c - 2aSubtract 5 from both sides
b + 5 - 5 = c - 2a - 5
b = c - 2a -5
Question 2: If m2 = p2 + 2a, make a the subject
m2 = p2+ 2a
Subtract p2 from both sides
m2 - p2 = p2 + 2a - p2
m2 - p2 = 2a
Divide both sides by 2
(m2 - p2)/2 = 2a/2
(m2 - p2)/2 = a
Why does 2a/2 = a?
(2 x a)/2= 2/2 x a = 1 x a = a