Download 5x - 2y are 5x and

Name:
Ms. D’Amato
Date:
Block:
Solving Two-Step/Multi-Step Equations
What does the word simplify mean?
Simplify each expression:
1. x + x + x + x = ________
2. y + y + y + y + y = ________
3. a + a = ________
4. c + c + c = ________
Name the coefficient for each expression above: 1. ____
2. ____
3. ____
4. ____
What is the coefficient of the term x? _____
Now, simplify: x + x + x + y + y
___________________. Put a box around each term.
Keep the sign with the number when you name terms. The terms of this expression:
5x  2y are 5x and 2y.
Name the terms of this expression:
3a  6b + c
When two terms have the EXACT SAME VARIABLE AND EXPONENT, they are called
______________.
Classify these terms by putting an L next to the like terms and a U next to the unlike terms:
6y, 2y _____ 3x, 2 _____
7y, 7x _____ 5x, x _____
3x2, 2x ______
When we simplify like terms, we combine their coefficients. For instance: 8x + 3x = 11x
Simplify:
6x + 2x ________
2x - 5x _______
6x + x _________
Are 6x and 2y like terms? ______ So: 6x + 2y = _________ When asked to simplify terms that are
not like, just write NP or NOT POSSIBLE.
For example:
2x + 7y cannot be simplified further. You would write NP
6x + 2y  4x can be written as 2x + 2y. You would stop!
You try! Underline the like terms. Then, simplify each expression. If the expression cannot be
changed, put NP.
1.
3x + 2 + 8x
2.
2
4
x +
x
7
7
3.
5 + 7x + 3
4.
5x − 11x
5.
3x + 5y + x
6.
3x + 2xy  x
7.
2y + 4x
8.
−4xy + 9xy
Solving Two-Step Equations:
1. Undo Addition or Subtraction (isolate the variable term)
2. Undo Multiplication or Division (make the variable’s coefficient = +1)
Study this example: 5x + 2 = 12 We have to undo both addition AND multiplication. The general rule
is to undo addition first (you are UNDOING, so you follow the order of operations BACKWARDS!!)
5x + 2 = 12
− 2 −2
5x = 10
5
5
x = 2
Check:
Undo addition
Undo multiplication
Show the First Step you would take in solving each equation:
1.
10 = 4x – 5
2.
-5 + 2x = 21
3.
x
 3  10
5
Let’s do the next example together:
7 + 3x = 28
Check:
This one is a little different! Notice that the coefficient of x is −1!! This requires special attention.
7 − x = 5
Try solving these:
1.
3x - 4 = -7
2.
x
 7  11
5
3.
−3 − 2x = 5
Solving Multi-Step Equations by Combining Like Terms:
1. Simplify one or both sides of the equation by Combining Like Terms
2. Undo Addition or Subtraction
3. Undo Multiplication or Division
Check your solution and reduce any fraction. No Decimals!
Consider this equation:
8+x−3=7
Notice the 8 and the  3 on the left hand side of the equation. They can be combined!
8 + x − 3 = 7
5 + x = 7
−5
−5
x = 2
Check:
Examples:
1.
3x + x = 64
2.
10 + 2x - 3 = 19
Try solving the following on your own:
3.
x + 8 + 2 = 7
4.
8 + x  2 = 8
5.
-4x + 7 + 2x = 19
6.
3
y
 7  1
8
Solving Multi-Step Equations Using the Distributive Property:
Simplify the following:
9(x + 3)
-(x + 6)
-4(3x – 4)
1
( x  12)
3
Simplify by combining the distributive property and like terms:
2(n – 7) + 4
4(3b + 5) – 4b
7x – 2(x – 5)
4 – 5(-4n + 3)
Once again, the general rule is to always simplify before undoing!
x + 3(x + 4) = 20
x + 3x + 12 = 20
4x + 12
= 20
 12
12
4x
= 8
4
4
x = 2
Eliminate parentheses by using the distributive property
Combine like terms
Undo addition (or subtraction)
Undo multiplication (or division)
We’ll solve one together and then you can try!
1.
7  4(d  3) = 23
2.
3.
5 - 3(-6x + 1) = 20
8a – 3(2a + 5) = 13
Solving Multi-Step Equations with Variables on Both Sides:
Look at this equation:
5x + 2 = 4x + 10
Do you see anything different with the variables? When variables are on different sides of the equals
sign, they CANNOT BE COMBINED! Move the variables to one side of the equal sign and constants
(numbers) to the other side of the equal sign.
5x + 2 = 4x + 10
7x + 14 = 5x
Try on your own to solve these:
1.
6x + 3 = 2x - 13
2.
6x + 3 = 4x + 19
3.
4(x  2) + 3x = 2x + 7
4.
5 − 2x = 3x
5.
24 - 3m = 5m + 6
6.
3(x + 2) + 2x = x + 36