Simplifying Equations

Simplifying Equations

Two ways to simplify equations:

• Combine like terms

• Use the distributive property

Combining Like Terms:

• Add together all the numbers

• Add together all the coefficients on x

• Coefficient = the number in front of x: 3 is the coefficient of 3x

8x + 3 + 6x + 4

• 8x + 6x = 14x

• 3 + 4 = 7

• 14x + 7

2x + 4 + 5x + 11

• 2x + 5x = 7x

• 4 + 11 = 15

• 7x + 15

Multiple Choice

6x + 4 + 5x + 7

• 6x + 11

• 11x + 11

• $x^2\ +\ 11$

Multiple Choice

6x + 2x + 7

• 8x + 7

• 8x

• 6x + 9

Multiple Choice

11x + x + 8 + 3

• 12x + 8

• 11x + 11

• 12x + 11

Multiple Choice

7x - 4 + 3x + 7

• 10x + 3

• 10x + 11

• 10x - 3

Multiple Choice

3x + 6 - x - 5

• 4x + 1

• 2x + 1

• 4x + 11

Using the Distributive Property

• Multiply what's in front of the parentheses by each number or symbol in the group

 $4\left(2x+3\right)$  

•  $4\cdot2x\ +\ 4\cdot3$  

•  $8x+12$  

 $-\left(x+3\right)$  

• The negative sign in front is the same as multiplying by -1

•  $\left(-1\cdot x\right)+\left(-1\cdot3\right)$  

•  $-x\ -\ 3$  

Multiple Choice

 $2\left(x+5\right)$  

• 2x + 7

• 2x + 10

• 2x + 5

Multiple Choice

 $\frac{1}{2}\left(4x+6\right)$  

• 8x + 12

• 4x - 6 

• 2x + 3

Multiple Choice

 $2\left(x+5\right)$  

• 2x + 7

• 2x + 10

• 2x + 5

Multiple Choice

 $-\left(-11x+1\right)$  

• 11x - 1

• -11x  - 1

• 11x + 1

Multiple Choice

 $2\left(x+1\right)$  

• x + 3

• 3x + 1

• 2x + 2