Combining like terms

Simplifying to solve Equations

The goal

​Please write this information in your notebook

The goal of solving an equation is to find the _________________ of the __________________

In order to do this we have to ___________________ the _____________________________

What's the big idea?

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There are two main ways we are going to simplify an equation in order to be able to solve it.
1. Combining like terms
2. Distribution

Steps of combining like terms

1. Identify what terms can be combined with each other. aka find the terms that are alike.

2. Understand the relationship between the sign in front of the number and how that is going to effect how it is combined with other terms

   1. to do this you can rewrite an expression and replace subtraction with the addition of a negative.

   2. By doing this you can draw a (charge) model to visualize the different terms and represent them as positive terms or negative terms.

3. COMBINE!!
   

Multiple Choice

2f + f

• 3f
• 2f
• f

Multiple Choice

Simplify the expression: 2x + 1 + 7x 

• 10x
• 10
• 9x + 1
• 9 + 1x

Multiple Choice

5x + 3y + 5 + 4x + 3y + y + 8

• 9x + 7y + 13
• 6x + 2y + 2
• 25x + 2y + 3
• x + 7y + 12

Multiple Choice

Collect like terms: 
4y + 8d - 2y + 3d

• 11d + 6y
• 11d + 2y
• 6y + 5d

Multiple Choice

Simplify the following expression
7 - 8c + 3 - 6c 

• -10+14c
• -25
• 10-14c
• 25c

Multiple Choice

-9n + 12n + 7

• 28n

• 10n

• 21n + 7

• 3n + 7

Multiple Choice

-6k + 7k=

• k
• -k
• 12k
• -12k

Multiple Choice

7 - 5m - 10m

• 7 + 15m

• 7 + 5m

• 7 - 5m

• 7 - 15m

Multiple Choice

Simplify the Expression:

3a + 7 - 2a

• 8a

• 12a

• a + 7

• 5a + 7

Multiple Choice

Find the equation that is equivalent to:
h + h + h + h + h + h + 4 + 4 = c

• 12h = c
• h + 8 = c
• 6h + 8 = c
• 8h + 6 = c

Multiple Choice

Simplify this equation by combining like terms.
2x+9+3x = m

• 5x+9 = m
• 14x = m
• 6x+9 = m

Multiple Choice

Find the equation that is equivalent to:
2 + 6 + w + w + w + -w + -w - 5 + 3 + -w = c

• 16 + 6w = c

• 16 = c

• 6 - w = c

• 6 = c

Multiple Choice

Which equation is equivalent to:
2x+11+6x = y

• 8x+11 = y
• 12x+11 = y
• 19x = y

Multiple Choice

Simplify the equation 2x + 1 + 7x = c

• 10x = c
• 10 = c
• 9x + 1 = c
• 9 + 1x = c

Multiple Choice

Simplify the equation 2 - 4x + 1 + 7x = y

• -3x + 3= y

• 11x + 3 = y

• 3x + 3 = y

• 3 - 11x = y

Multiple Choice

Simplify the equation 5n - 2n + 8 - n + 10n - 3 = k

• 12n + 5 = k

• 12n + 11 = k

• 14n + 5 = k

• 18 - n = k