Download Solve Multi-Step Equations

Notes 7-1
Solving Two – Step Equations
Example
2x − .4
= 8
+. 4 = + .4
2x = 8.4
2 = 2
First you UNDO addition and subtraction.
Second you UNDO multiplication and division.
. .
This is your solution – – – –>
Vocabulary
inverse operation
solution
justify
x = 4.2
Description
UNDO Do the opposite to both sides of the equal sign (the RIVER)
answer - must be in [x = ____ ] form
tell which operation/property is used for each step
STEPS
Another Example
1. Identify your variable.
2y + .2 = 11
2. “What + or – are they doing to your variable?”
..
3. UNDO – Use the inverse operation
– .2 = – .2
TO BOTH SIDES of the equal sign.
..
4. “What x or ÷ are they doing to your variable?”
2y = 10.8
5. UNDO – Use the inverse operation
TO BOTH SIDES of the equal sign.
6. Solve.
2
=
2
The variable is “y”.
They are adding .2
SUBTRACT .2 from both sides of equation.
They are multiplying by 2.
Divide by 2 on both sides of equation.
.
y = 5.4
Negative coefficients
– x could mean subtract x or add – x, These are the same. – x means the number in front of the variable is –1 .
To solve for x , divide both sides by – 1 . (Multiplying both sides by – 1 does the same thing.)
Example
12 – 3x = 18 The 12 is NOT subtracted. It is a positive 12. Adding 12 will just make it BIGGER = 24.
– 12
– 12 subtract 12 from both sides
-3x = 6
-3 -3 then divide both sides by – 3.
x = -2
Notes 7-2
Solving Multi – Step Equations
remember: The opposite of division is multiplication.
The opposite of multiplication is division.
You may need to combine like terms before you use inverse operations. Gather your (_) together first.
To help you with this, put a box around terms with the [same variable], and circle (constants)
INCLUDE the operation sign in front of each.
Distributive Property – multiply the first number AND multiply the SECOND number.
Example
2y – 3 + 3y = 12
Description of STEPS
1. Identify and box your variable.
The variable is “y”.
..
2y (– 3) + 3y = (12)
.
2. Combine the like terms.
add 2y and 3y
5y (– 3) = (12)
.
+3 = +3
3. UNDO + or – Use the inverse operation
Add 3 to both sides.
..
5y = 15
5
. 5
y = 3
4. UNDO x or ÷ Use the inverse operation
Divide both sides by 5.
5. Solve.