7th Unit 2 Review

7th Unit 2 Review

Equations and Inequalities

Properties (EE.1)

• Associative - same terms, same order, different grouping 

   $10\ +\ 20\ +\ 30\ =\ 10\ +\ \left(20\ +\ 30\right)$  

• Commutative - same terms, different order  $10\ +\ 20\ +\ 30\ =\ 30\ +\ 10\ +\ 20$  

• Distributive - different terms on each side $10\ \left(20\ +\ 30\right)\ =\ 200\ +\ 300$  

• Identity - Same terms, but a 1 or 0 is missing from one side $10\ +\ \ 0\ +\ 20\ =\ 10\ +\ 20$  

Multiple Choice

Which property states these two expressions are equal?

 $2x\ +\ 1y\ \ =\ \ 2x\ +\ y$  

• Associative

• Commutative

• Distributive

• Identity

Multiple Choice

Which property states these two expressions are equal?

 $2\ +\ 6a\ +\ b\ \ =\ 2\ +\ \left(6a\ +\ b\right)$  

• Associative

• Commutative

• Distributive

• Identity

Multiple Choice

Which property states these two expressions are equal?

 $2\ +\ 6a\ +\ b\ \ =\ 6a\ +\ b\ +\ 2$  

• Associative

• Commutative

• Distributive

• Identity

Multiple Choice

Which property states these two expressions are equal?

 $2\ \left(6a\ +\ b\ \right)\ =\ 12a\ +\ 2b$  

• Associative

• Commutative

• Distributive

• Identity

Simplify the Expression (EE.2)

• Combine all the like terms x², x, y, 8

• You can only combine terms with the same variable to the same power.

•  $1\ +\ 2\ +\ 3x\ +\ 4x$  

  = 3 + 7x

Multiple Choice

Simplify: $3x\ +\ 4\ +\ 2x\ +\ 10$ 

• 19x

• 6x + 14

• 5x + 14

• 70x

Multiple Choice

Distribute to find the equivalent expression

 $8\left(3x\ +\ 7\right)$  

• 24x + 56

• 80x

• 24x + 7

• 168x

Multiple Choice

Simplify:

 $3\ +\ 5x\ -\ 10\ -x$  

• -4x - 7

• 4x + 7

• -4x + 7

• 4x - 7

Multiple Select

Which three are equivalent expressions?

• 2b + 4b + 6b

• 12b

• 2 (b + 2b + 3b)

• 6b + 6

Multiple Select

Factor to find all 3 equivalent expressions:

 $12x\ -\ 18$  

• 2 (6x - 9)

• 3 (4x - 6)

• 6 (2x - 3)

• 2 (6x + 9)

• 3 (4x - 18)

Solving Equations (EE.3)

• Simplify the equation (only one variable)

• Isolate the variable by using inverse operations

• OUR Method or Balanced Scale (Backwards OOO)

Multiple Choice

Solve:

 $\frac{x}{6}\ -\ 9\ =\ 9$  

• x = 0

• x = 3

• x = 108

• x = 102

Multiple Choice

Solve:

12 - 4x = 24

• x = 3

• x = -3

• x = 16

• x = -16

Multiple Choice

Solve:

 $5x\ +4\ =\ 59$  

• x = 9

• x = 10

• x = 11

• x = 12

Multiple Choice

Solve:

 $7x\ =\ 4x\ +\ 39$  

• x = 10

• x = 11

• x = 12

• x = 13

Multiple Choice

Solve:

 $3b\ +\ 12\ =\ 48\ -\ 6b$  

• b = 4

• b = -4

• b = 12

• b = -12

Solving Inequalities (EE.4b)

• Simplify the expression

• Isolate the variable by inverse operation

• OUR method or balanced scale

• ONLY change the sign if you multiply or divide by a negative value

Multiple Choice

Solve:

 $7x\ >\ 49$  

• x > 7

• x < 7

• x > -7

• x < -7

Multiple Choice

Solve:

 $\frac{x}{2}\ +\ 3\ <\ 9$  

• x < 3

• x < 12

• x < 6

• x < 9

Multiple Choice

Solve:

 $\frac{x}{5}\ -\ 12\ \ge\ -22$  

•  $x\ \ge\ -50$  

•  $x\ \le\ -50$  

•  $x\ \ge\ -2$  

•  $x\ \le\ -2$  

Multiple Choice

Solve:

 $-2x\ +\ 13\ >\ 21$  

• x > -16

• x < -16

• x > -4

• x < -4

Multiple Choice

Solve:

-4 (x + 2) < 0

• x < 2

• x < -2

• x > 2

• x > -2

Writing Inequalities (EE.4c)

• Look for KEY WORDS that set the limits

•  $>$   greater than, more than, exceed, larger than

•  $<$   less than, smaller than

•  $\ge$  greater than or equal to, at least, minimum

•  $\le$  less than or equal to, at most, maximum

Multiple Choice

Stacy's parents tell her she can spend, at most, $60 on new shoes. Which inequality represents the amount she can spend?

• $x\ >\ 60$

• $x\ <\ 60$

• $x\ \ge\ 60$

• $x\ \le\ 60$

Multiple Choice

Goofy has more than 6 speeding tickets. Which inequality matches?

• $x\ <\ 6$

• $x\ >\ 6$

• $x\ \ge\ 6$

• $x\ \le\ 6$

Multiple Choice

Hallie was told she had to get a minimum of 10 people to join her to create her own club at the school. Which inequality matches?

• x > 10

• x < 10

• $x\ \ge\ 10$

• $x\ \le\ 10$

Multiple Choice

Lenny got less than $200 on his last paycheck.

• x > 200

• x < 200

• $x\ \ge\ 200$

• $x\ \le\ 200$

Writing Equations (EE.4a)

• Look for KEY WORDS

• + gain, add, ascend, (sum)

• - lose, subtract, descend, (difference)

• x multiply, times, double, (product)

• / divide, a forth, half, (quotient)

Multiple Choice

Mark has read 245 pages in a 505 page book. If he reads 15 pages a day, how many days will it take to finish the book?

• 245p + 15 = 505

• 245 + 15p = 505

• 260p = 505

• 245 - 15p = 505

Multiple Choice

Tucker scored 32 points in today's game. This was 4 more than twice the amount of points Sal made.

• 32 = 4 + 2x

• 32 + 4 = 2x

• 32 + 2x = 4

• 2 + 4x = 32

Multiple Choice

Herbert spent $203 on 17 video games. If he spent the same amount on each game, which equation could we use to find how much he spent on each one?

• 17x = 203

• $\frac{x}{17}=\ 203$

• 17 + x = 203

• x - 17 = 203

Multiple Choice

Paul bought a bag of chips for $3 and grapes for $2 per pound. If he spent a total of $16, which equation could we use to find the weight of the grapes?

• 16 + 2x = 3

• 5x = 16

• 3x + 2 = 16

• 3 + 2x = 16

Graphing Inequalities  (6.EE.8)

•  $>$   OPEN circle and line is to the right

•  $<$  OPEN circle and line is to the left

•  $\ge$  CLOSED circle and line is to the right

•  $\le$  CLOSED circle and line is to the left

Multiple Choice

Which inequality matches the graph?

• x < 80

• x > 80

• $x\ \ge\ 80$

• $x\ \le\ 80$

Multiple Choice

Which inequality matches?

• x > 6

• x < 6

• $x\ \ge\ 6$

• $x\ \le\ 6$

Multiple Choice

Which inequality matches?

• x > 100

• x < 100

• $x\ \ge\ 100$

• $x\ \le\ 100$

Multiple Choice

Which inequality matches?

• x > 80

• x < 80

• $x\ \ge\ 80$

• $x\ \le\ 80$