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Linear equations
1.
2. 1-step Equations: + and – 2/27/13
In elementary school, you solved
equations that looked like this:
In Algebra, we just use a variable
instead of the box!
We could rewrite the same equation
like this: x + 3 = 5
3. To solve:
Need to get x by itself.
We must “undo” whatever has been done
to the variable.
Do the same to BOTH SIDES of the = sign!
Answer should be: x = some number.
4. Equations Have to Balance!
Both sides of the = sign must “weigh” the
same!
When you change one side, do the same
to the other side, so it stays balanced!
x + 3 = 7
9. 1-step Equations: × and ÷ 3/11/13
Just like with adding and subtracting,
we need to “undo” what is done to x.
Use division to “undo” multiplication.
Use multiplication to “undo” division.
Remember: A fraction bar means
divide!
Example: says x divided by 3!
13. Basic 2-Step Equations 3/13/13
A lot like 1-step equations!
Goal: Get x by itself!
Need to “undo” what is done to x.
Always do the same thing to BOTH SIDES!
Use Order of Operations backwards:
Add/Subtract first
Multiply/Divide last
21. 2 Variables- Same Side 3/21/13
Some equations have variables in more
than one place.
When variables are on the same side of
the = sign:
First, Combine Like Terms
Like terms may NOT cross the = sign!
Then, solve like a 2-step
26. Variables on Both Sides 3/22/13
To solve equations like this:
2x – 4 = 2 + 5x
1. Get variables together on the left.
Add or subtract right side x term from
both sides.
2. Solve like a 2-step equation.