Transcript Solving 2-Step Equations

Combining Like Terms
Unit 2, Lesson 5
Online Algebra 1
VHS@pwcs
Like Terms
 Like terms are terms with exactly the same
variable and the same exponent on that
variable.
 The following are examples of like terms.
Notice that they have all the same variables
and same exponents:



4x and -2x
-24xy3 and xy3
16a2 and 11a2
 We can add and subtract like terms.
 We can multiply and divide like and unlike
terms.
Unlike Terms
 Unlike terms do not have the same
variable or the same exponent on that
variable..
 They cannot be added or subtracted.
 Below are examples of unlike terms




5t and y
-2x and 4x3
3xy and 7x4y
3a and 3a2
Combining Like terms.
 To add or subtract like terms.
1.
2.

Add/subtract the coefficient, number in
front of the variable.
Keep the variable the same.
Examples:
1.
3x + 9x

2.
(3 + 9)x = 12x
-8x + 11x + 12

(-8 + 11)x + 12 = 3x + 12
Simplify these on your own.
1.
2n – 3n
2.
b – 8b + 9
3.
17v + 8
4.
14r + 8s – 19r
1.
-1n or –n, remember or
super hero, the invisible
1
2.
-7b + 9
3.
17v + 8, or we can say
already simplified.
4.
-5r + 8s
Solving Equations Involving
Like Terms.
Recall the following steps we use to solve 2-step
equations:
1. If the equation involves subtraction, change
the equation to addition.
2. Undo any addition, by adding the opposite to
both sides.
3. Undo multiplication and division by using
inverse operations.
4. Check by substituting your value in for the
variable and simplifying. If you get a true
statement you are correct, if not go back and
check your math.
Solving Equations Involving
Like Terms.
Not all steps
are needed
for all
equations.
The steps
are a
general
guideline!
In order to solve equations with like terms, we add the
following step.
1.
If the equation involves subtraction, change the
equation to addition.
2.
Combine like terms if any.
3.
Undo any addition, by adding the opposite to both
sides.
4.
Undo multiplication and division by using inverse
operations.
5.
Check by substituting your value in for the variable
and simplifying. If you get a true statement you are
correct, if not go back and check your math.
Solve: 3m + 4.5m = 15
1.
If the equation involves subtraction, change the
equation to addition. There is none so we can skip
this step.
2.
Combine like terms if any. This we will use
3.
Undo any addition, by adding the opposite to both
sides. There is no addition so we skip this step
too.
4.
Undo multiplication by dividing both sides by 7.5.
5.
Check by substituting your value in for the variable
and simplifying. If you get a true statement you are
correct, if not go back and check your math.
3m + 4.5m = 15
7.5m = 15
7.5 7.5
m=2
Check:
3(2) + 4.5(2) = 15
6 + 9 = 15
15 = 15
Solve 7m – 3m - 6 = 6
1.
Change the subtraction to addition.
2.
Combine like terms
3.
Undo any addition by adding 6 to both sides.
4.
Undo multiplication by dividing both sides by 4
5.
Check by substituting your value in for the
variable and simplifying. If you get a true
statement you are correct, if not go back and
check your math.
7m – 3m – 6 = 6
7m + -3m + -6 = 6
4m + -6 = 6
6 6
4m = 12
4 4
m=3
Check:
7(3) – 3(3) – 6 = 6
21 – 9 – 6 = 6
12 – 6 = 6
6=6
Try These On Your Own!
3x -7 + x = 5
3x + -7 + x = 5
4x + -7 = 5
7 7
4x = 12
4 4
x=3
x + 5x – 5 = 1
x + 5x + -5 = 1
6x + -5 = 1
5 5
6x = 6
6 6
x=1
Check:
3(3) – 7 + 3 = 5
9–7+3=5
2+ 3 = 5
5=5
Check:
1 + 5(1) – 5 = 1
1+5–5=1
6–5=1
1=1
Review Steps To Solving
Equations.





If the equation involves subtraction, change
the equation to addition.
Combine like terms if any.
Undo any addition, by adding the opposite to
both sides.
Undo multiplication and division by using
inverse operations.
Check by substituting your value in for the
variable and simplifying. If you get a true
statement you are correct, if not go back and
check your math.