Download Notes for 1Z: Solving Equations By Grouping Like Terms First

Notes for 1Z: Solving Equations By Grouping
Like Terms First
Equations with multiple 'x' terms in it
Sometimes we have multiple 'x' terms in an equation. For example: x + 2x = 6.
But if we remember that x + 2x is really just 3x. So the equation is just 3x = 6.
So, when we have equations with multiple 'x terms in it, we should just ADD LIKE TERMS.
Then when we have only one overall 'x' term left, we can solve as we have always done.
Examples:
Solve 4x + 7x = 44.
Solution:
4x + 7x = 44
11x = 44
(add the x terms on the LHS)
Now solve
x = 4 (however you choose to solve it)
Solve 5x + 3x + 2 = 26
Solution:
5x + 3x + 2 = 26
8x + 2 = 26 (add the x terms on the LHS)
Now solve
8x = 24
x=3
In addition to there sometimes being multiple 'x' terms on one side, sometimes there can be
multiple numbers on the one side. Again, we can combine all the numbers (add and subtract) to
simplify to one number, before we attempt to solve.
Example:
Solve 3x + 2x + 7 + 3 = 60
Solution:
3x + 2x + 7 + 3 = 60
5x + 10 = 60 (3x + 2x = 5x, AND 7 + 3 = 10)
Now solve
5x + 10 = 60
5x = 50
x = 10
Sometimes, we have multiple expressions and only KNOW the total.
For example, we might have 3 expressions:
x
3x + 1
2x – 3
We don't know what any of these expressions are equal to, but we do know the total is
something... let's say 10.
Then we can say this:
(x) + (3x + 1) + (2x – 3) = 10.
Notice I have just added all 3 expressions together and made it equal to 10.
The brackets are useful when “putting it all together” but afterwards are not needed, so the
equation can quickly becomes
x + 3x + 1 + 2x – 3 = 10.
Then we can simplify by grouping our 'x' terms and grouping our number terms.
We get 6x – 2 = 10
Then we solve
(x + 3x + 2x = 6x AND 1 – 3 = -2)
6x – 2 = 10
6x = 12
x=2
This is a very useful strategy for solving some worded questions.