Questions

1. Which of the following is an algebraic expression?
   
   • 2x + 2
     
   • x + 2 & 8
     
   • x÷2 + 6 - x
     
   • 5 - 3 # x
     
   • (x + 3)÷2
     
   • - x÷8

2. What is the coefficient of the term in x in the following algebraic expressions?
   
   • 2x - 7
     
   • x/2 - 10
     
   • - x + 7
     
   • x + 7
     
   • - x÷4

3. What is the value of 2x + 7 for the given values of x?
   
   • x = - 1
     
   • x = - 4
     
   • x = 0
     
   • x = 5

4. What is the value of the expression x÷3 - 9 for the given values of x?
   
   • x = 0
     
   • x = 3
     
   • x = 9
     
   • x = - 12

5. What is the value of the expression (- x + 2) ÷2 + 1 for the given values of x?
   
   • x = 0
     
   • x = 2
     
   • x = - 2
     
   • x = - 12

6. What is the value of the expression 12 x - 3 for the given values of x?
   
   • x = 1/2
     
   • x = 1/6
     
   • x = - 3/4
     
   • x = - 1÷4

7. What is the value of the expression - 0.1 x + 2.5 for the given values of x?
   
   • x = 1
     
   • x = - 1
     
   • x = 2
     
   • x = - 2

8. Which of the following expressions has the largest value for x = - 3?
   
   • x + 10
     
   • - x + 10
     
   • x÷3 + 10
     
   • - x÷3 + 10

9. Which of the following shows the commutative property of the addition?
   
   • a + b = b - a
     
   • a + b = b a
     
   • a + b = a÷b
     
   • a + b = b + a

10. Which of the following shows the associative property of the addition?
    
    • a + b = b + a
      
    • (a + b) + c = c + (a + b)
      
    • a + ( b + c ) = (a + b) + c
      
    • a + ( b + c ) = (a + b) - c

11. Which of the following expressions is equivalent to the algebraic expression 3x + 2 - x + 4?
    
    • 6
      
    • 4x + 6
      
    • 2x + 6
      
    • 3x² +6

12. Which of the following algebraic expression is a mathematical representation to the statement "2 times x plus 20".
    
    • 2 + x + 20
      
    • 2 x + 20
      
    • 2 - x + 20
      
    • 2 ÷ x + 20

13. Which of the following algebraic expression is a mathematical representation to the statement "Three times x subtracted from 17".
    
    • 3x - 17
      
    • 17 - 3x
      
    • 3x + 17
      
    • 17+3x

14. Jo has has x cards. Janette has 10 cards more that Jo. Write an algebraic expression that indicates how many cards Janette has.
    
    • 10 x
      
    • x - 10
      
    • x + 10
      
    • x÷10

15. Carla had 20 toy cars. She lost x toy cars lately. Write an algebraic expression that indicates how many toy cars Carla has now.
    
    • 10 x
      
    • x - 10
      
    • x + 10
      
    • x÷10

16. Chris had $200. He spent $20 on food and he bought a book at the price of a dollars. Write an algebraic expression that indicates how much money chris has left.
    
    • 200 + 20 - a
      
    • 200 - 20 - a
      
    • 20 + a - 200
      
    • 200 + a + 20

17. Nathan had x cards and he gave half to Tanya and Tanya gave a third of her card to Salma. Write an algebraic expression that indicates the number of cards Tanya has.

Solutions to the Above Questions and Problems

1. 
   solution
   Algebraic expressions contain real numbers, variables and one or many of the the 4 mathematics operators (+ , - , × , ÷ or /). Hence the following are algebraic expressions:
   2x + 2 , x÷2 + 6 - x , (x + 3)÷2 , - x÷8
   Note: 2x means 2 × x
   The following are not algebraic expressions.
   x + 2 & 8 : it contains the character & which is not a number, neither a variable nor a mathematical operator.
   5 - 3 # x : it contains the character # which is not a number, neither a variable nor a mathematical operator.
2. 
   solution
   To find the coefficient of a term in x (or any other variable), isolate the term in x and write it as a multiplication and the real number involved in the multiplication is the coefficient of the term.
   

   expression	term in x	write as a multiplication	find coefficient
   2x - 7	2x	2×x	2
   x/2 - 10	x÷2	(1/2)×x	1/2
   - x + 7	- x	(-1)×x	- 1
   x + 7	x	(1)×x	1
   - x/4	- x÷4	(-1/4)×x	- 1/4

3. 
   solution
   To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   2x + 7	-1	2 × (-1)+7=	-2 + 7 = 5
   2x + 7	- 4	2 × (-4)+7=	- 8 + 7 = - 1
   2x + 7	0	2 × (0)+7=	0 + 7 = 7
   2x + 7	5	2 × (5)+7=	10 + 7 = 17

4. 
   solution
   To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   x ÷ 3 - 9	0	(0) ÷ 3 - 9=	0 - 9 = - 9
   x ÷ 3 - 9	3	(3) ÷ 3 - 9 =	1 - 9 = - 8
   x ÷ 3 - 9	9	(9) ÷ 3 - 9 =	3 - 9 = - 6
   x ÷ 3 - 9	- 12	(-12) ÷ 3 - 9 =	- 4 - 9 = - 13

5. 
   solution
   To evaluate an algebraic expression for a given numerical value of x, substitute x in the expression by its numerical value and evaluate the expression.
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   (- x + 2) ÷ 2 + 1	0	(- (0) + 2) ÷ 2 + 1 =	= (0 +2) ÷ 2 + 1 = 2 ÷ 2 + 1 = 1 + 1 = 2
   (- x + 2)÷2 + 1	2	(-(2) + 2)÷2 + 1 =	(-2 + 2)÷2 + 1 = 0÷2 + 1 = 0 + 1 = 1
   (- x + 2)÷2 + 1	-2	(- (- 2) + 2)÷2 + 1 =	(2 + 2 )÷2 + 1 = 4/2 + 1 = 2 + 1 = 3
   (- x + 2)÷2 + 1	- 12	(- (-12) + 2)÷2 + 1 =	(12 + 2)÷2 + 1 = 14/2 + 1 = 7 + 1 = 8

6. 
   solution
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   12 x - 3	1/2	12 (1/2) - 3 =	= 12÷2 - 3 = 4 - 3 = 1
   12 x - 3	1/6	12 (1/6) - 3 =	= 12÷6 - 3 = 2 - 3 = - 1
   12 x - 3	-3/4	12( - 3/4) - 3 =	= - 36÷4 - 3 = - 9 - 3 = - 12
   12 x - 3	-1/4	12 (-1/4) - 3 =	= -12÷2 - 3 = - 6 - 3 = - 9

7. 
   solution
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   - 0.1 x + 2.5	1	- 0.1 × (1) + 2.5 =	= -0.1 + 2.5 = 2.4
   - 0.1 x + 2.5	- 1	- 0.1 × ( - 1) + 2.5 =	= 0.1 + 2.5 = 2.6
   - 0.1 x + 2.5	2	- 0.1 × (2) + 2.5 =	= -0.2 + 2.5 = 2.3
   - 0.1 x + 2.5	- 2	- 0.1 × (-2) + 2.5 =	= 0.2 + 2.5 = 2.7

8. 
   solution
   

   expression	value of x	substitute x in expression by its value using brackets	evaluate
   x + 10	- 3	(-3) + 10 =	= - 3 + 10 = 7
   - x + 10	- 3	- (-3) + 10 =	= 3 + 10 = 13
   x÷3 + 10	- 3	(-3)÷3 + 10 =	= - 1 + 10 = 9
   - x÷3 + 10	- 3	- (-3)÷3 + 10 =	= 3÷3 + 10 = 1 + 10 = 11

   
   The algebraic expression - x + 10 has the largest value 13 for x = - 3.
9. 
   solution
   The commutative property of the addition is given by:
   a + b = b + a
10. 
    solution
    The associative property of the addition is given by:
    a + ( b + c ) = (a + b) + c
11. 
    solution
    All the expressions are in simplified form and therefore we first need to simplify the given expression by grouping like terms.
    3x + 2 - x + 4 = 3x - x + 2 + 4 = 2 x + 6
    Expression 3x + 2 - x + 4 is equivalent to 2 x + 6.
    
12. 
    solution
    We convert ""2 times x plus 20". " to a mathematical expression by steps.
    "2 times x " is mathematically represented by : 2 × x = 2 x
    "2 times x plus 20" is mathematically represented by : 2 x + 20
    
13. 
    solution
    We convert "Three times x subtracted from 17" to a mathematical expression by steps.
    "Three times x " is mathematically represented by : 3 × x = 3 x
    "Three times x subtracted from 17" is mathematically represented by : 17 - 3x
    
14. 
    solution
    Jo has x cards.
    Jo : x
    "Janette has 10 cards more that Jo" is mathematically represented by :
    x + 10
15. 
    solution
    Carle starts with 20 toy cars.
    Carla : 20
    What is lost is subtracted from the total number of toys. Hence since she lost x toys,
    20 - x car toys are left.
16. 
    solution
    Chris starts with $200.
    Chris : $200
    He spent $20 on food and therefore we need to subtract it from the total
    Chris : $200 - $20 after buying the food
    He spent a dollars on books and therefore we need to subtract it from 200 - 20
    Chris : $200 - $20 - a , the money that Chris has after bying food and a book.
17. 
    solution
    Nathan has x cards
    Nathan : x
    Nathan gave half of his cards to Tanya and so Tanya has
    Nathan to Tanya : (1/2) x
    If Tanya gave 1/3 of her cards to Salma, she is left with 2/3 of the cards given to her by Nathan. Hence Tanya has
    (2/3)((1/2) x) = ( 2/6) x cards

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