Foundations of Algebra Review

Foundations of Algebra Review

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Combining Integers

• Adding and Subtracting: Remember SADS

• Same Sign: ADD!! 1 + 3 = 4; (-5) - 10 = -15

• Different Sign: SUBTRACT!! (-9) + 4 = -5; 6 - 4 = 2

• Multiplying and Dividing: Negative Rules

• (+)*(+) = (+); (-)*(-) = (+)

• (-)*(+) = (-); (+)*(-) = (-)

Multiple Choice

-3 +(- 2)

• -1
• 5
• -5
• -6

Multiple Choice

-5 - (- 3)

• -8
• 8
• -2
• 15

Multiple Choice

-9 - 5

• -14
• 4
• -4
• 45

Multiple Choice

6 - (-4)

• 10
• 2
• -2
• -10

Combining Like Terms

• Like Terms have the same variable and the same exponent

• 2x + 5x => 7x

• 3 + 4n + 7 - 3n => 10 + n

• 
  
   $6c^2-10c^2+10c\ \ \rightarrow\ -4c^2+10c$  
  

Multiple Choice

Simplify by combining like terms:

5a + 2b - 3a + 4

• 8a + 2b + 4

• 2a + 2b + 4

• 8ab

• 4ab + 4

Multiple Choice

• 6x-1

• 10x+7

• 6x+1

• 8x+1

Multiple Choice

• 8y+5

• 3y+3

• 7y+5

• 7y+4

Properties of Equality

• Addition Property of Equality

• if a = b, then a + c = b + c

• Subtraction Property of Equality

• if a = b, then a - c = b - c

• Example: x - 6 = 13

• x - 6 + 6 = 13 + 6

• x = 19

Properties of Equality

• Multiplication Property of Equality

• if a = b, then a*c = b*c

• Division Property of Equality

• if a = b, then

   $\frac{a}{c}=\frac{b}{c}$  

• Example: 7n = 84

•  $\frac{7n}{7}=\frac{84}{7}$  

• n = 12

Multiple Choice

Which property of equality should be used to solve the equation below?

 $-12+x=19$  

• Addition

• Subtraction

• Multiplication
  

• Division

Multiple Choice

Which property of equality should be used to solve the equation below?

 $\frac{n}{10}=1.4$  

• Addition

• Subtraction

• Multiplication
  

• Division

Solving Multi-Step Equations

• If necessary, simplify Left and Right sides of equations separately by combining like terms (Remember PEMDAS)

• Use Properties of Equality to isolate the variable.

• Example: 2x + 3 = -7 (Original Equation)

• 2x + 3 - 3 = -7 - 3 (Subtraction Property of Equality)

• 2x = -10 (Combine Like Terms)

• 
  
   $\frac{2x}{2}=-\frac{10}{2}$  (Division Property of Equality)
  

• x = -5 

Another Example:

 $13\ =\ 3\left(x-1\right)+x$  

•  $13=3x-3+x$  (Distributive Property)

•  $13=4x-3$  (Combining Like Terms)

•  $13+3=4x-3+3$  (Addition Property of Equality)

•  $16=4x$  (Combining Like Terms)

•  $\frac{16}{4}=\frac{4x}{4}$  (Division Property of Equality)

•  $4=x$  (Simplify)

•  $x=4$  (Symmetric Property)

Multiple Choice

What is the first step in solving the equation 2a - 4(a - 5) = 10

• Add 4 to both sides

• Add the 2a and a

• Distribute 4 to a and -5

• Distribute -4 to a and -5

Multiple Choice

33 = 4a - 7

• a=-10
• a=10
• a=4.5

Multiple Choice

4(a + 3) = -32

• -11
• -44
• -20
• -8

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