Simplifying formulas » Rearranging and substituting formulas  


Rearranging formulas

You can use the balance method to rearrange a formula.
In formula q = 5p + 7  is q expressed in terms of p.
In formula a = 4b2 + 1  is a expressed in terms of b.

Example 1
Given is the formula 5q + 20p = 45
Rearrange this formula so q is expressed in terms of p.

Answer:

 5q + 20p = 45
q + 4p = 9
q = –4p + 9

Example 2
Given is the formula 2(4a – 6) + 5b = 4
Rearrange this formula so a is expressed in terms of b.

Answer:

 2(4a – 6) + 5b = 4
8a – 12 + 5b = 4
8a = –5b + 16
a = –58b + 2

Substituting formulas

Substituting is change a variable in a formula with another formula.
After you substituted you shorten the formula.
Important: The formule you are substituting will be between brackets.

Example 1
Substitute formula B into formula A.
A: y = 6t + 12 and B: t = 3x + 4

Answer:

y = 6t + 12
y = 6(3x + 4) + 12
y = 18x + 24 + 12
y = 18x + 36

Example 2
Substitute formula B into formula A.
A: p = 3q – 2 and B: q = 4a + 7

Answer:

p = 3q – 2
p = 3(4a + 7) – 2
p = 12a + 21 – 2
p = 12a + 19